06 Apr 2022

Samacheer kalvi 10th Maths – Algebra Ex 3.15

10th Maths Book Back Question and Answers – Chapter 3 Exercise 3.15:

Samacheer Kalvi 10th Standard Maths Book Back Questions with Answers PDF uploaded and the same given below. Class-tenth candidates and those preparing for TNPSC exams can check the Maths Book Back Answers PDF below. Samacheer Kalvi Class 10th Std Maths Book Back Answers Chapter 3 Exercise 3.15 Solutions are available below. Check the complete Samacheer Kalvi 10th Maths – Algebra Ex 3.15 Book Back Answers below:

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Samacheer Kalvi 10th Maths Book Back Answers – Ex 3.15 Algebra

Samacheer Kalvi 10th Maths Book Subject One Mark, Two Mark, Five Mark Guide questions and answers are below. Check Maths Book Back Questions with Answers. Take the printout and use it for exam purposes.

For Samacheer Kalvi 10th Maths Book PDF, check the link – 10th Maths Book PDF

Chapter 3

Exercise 3.15 Algebra

1. Graph the following quadratic equations and state their nature of solutions,
(i) x2 – 9x + 20 = 0
Solution:
10th maths unit - 3 book back answer

Step 1:
Points to be plotted : (-4, 72), (-3, 56), (-2, 42), (-1, 30), (0, 20), (1, 12), (2, 6), (3, 2), (4, 0)
Step 2:
The point of intersection of the curve with x axis is (4, 0)
Step 3:

10th maths unit - 3 book back answer

The roots are real & unequal
∴ Solution {4, 5}

(ii) x2 – 4x + 4 = 0
10th maths unit - 3 book back answer

Step 1: Points to be plotted : (-4, 36), (-3, 25), (-2, 16), (-1, 9), (0, 4), (1, 1), (2, 0), (3, 1), (4, 4)
Step 2: The point of intersection of the curve with x axis is (2, 0)
Step 3:
10th maths unit - 3 book back answer

Since there is only one point of intersection with x axis, the quadratic equation x2 – 4x + 4 = 0 has real and equal roots.
∴ Solution{2, 2}

(iii) x2 + x + 7 = 0
Let y = x2 + x + 7
Step 1:
10th maths unit - 3 book back answer

Step 2:
Points to be plotted: (-4, 19), (-3, 13), (-2, 9), (-1, 7), (0, 7), (1, 9), (2, 13), (3, 19), (4, 27)
Step 3:
Draw the parabola and mark the co-ordinates of the parabola which intersect with the x-axis.
10th maths unit - 3 book back answer

Step 4:
The roots of the equation are the points of intersection of the parabola with the x axis. Here the parabola does not intersect the x axis at any point.
So, we conclude that there is no real roots for the given quadratic equation,

(iv) x2 – 9 = 0
Let y = x2 – 9
Step 1:
10th maths unit - 3 book back answer

Step 2:
The points to be plotted: (-4, 7), (-3, 0), (-2, -5), (-1, -8), (0, -9), (1,-8), (2, -5), (3, 0), (4, 7)
Step 3:
Draw the parabola and mark the co-ordinates of the parabola which intersect the x-axis.

10th maths unit - 3 book back answer

Step 4:
The roots of the equation are the co-ordinates of the intersecting points (-3, 0) and (3, 0) of the parabola with the x-axis which are -3 and 3 respectively.
Step 5:
Since there are two points of intersection with the x axis, the quadratic equation has real and unequal roots.
∴ Solution{-3, 3}

 

(v) x2 – 6x + 9 = 0
Let y = x2 – 6x + 9
Step 1:
10th maths unit - 3 book back answer

Step 2:
Points to be plotted: (-4, 49), (-3, 36), (-2, 25), (-1, 16), (0, 9), (1, 4), (2, 1), (3, 0), (4, 1)
Step 3:
Draw the parabola and mark the co-ordinates of the intersecting points.

10th maths unit - 3 book back answer

Step 4:
The point of intersection of the parabola with x axis is (3, 0)
Since there is only one point of intersection with the x-axis, the quadratic equation has real and equal roots. .
∴ Solution (3, 3)

(vi) (2x – 3)(x + 2) = 0
2x2 – 3x + 4x – 6 = 0
2x2 + 1x – 6 = 0
Let y = 2x2 + x – 6 = 0
Step 1:
10th maths unit - 3 book back answer

Step 2:
The points to be plotted: (-4, 22), (-3, 9), (-2, 0), (-1, -5), (0, -6), (1, -3), (2, 4), (3, 15), (4, 30)
Step 3:
Draw the parabola and mark the co-ordinates of the intersecting point of the parabola with the x-axis.

10th maths unit - 3 book back answer

Step 4:
The points of intersection of the parabola with the x-axis are (-2, 0) and (1.5, 0).
Since the parabola intersects the x-axis at two points, the, equation has real and unequal roots.
∴ Solution {-2, 1.5}

 

2. Draw the graph of y = x2 – 4 and hence solve x2 – x – 12 = 0
Solution:
10th maths unit - 3 book back answer

10th maths unit - 3 book back answer

10th maths unit - 3 book back answer

Point of intersection (-3, 5), (4, 12) solution of x2 – x – 12 = 0 is -3, 4

3. Draw the graph of y = x2 + x and hence solve x2 + 1 = 0.
Solution:
10th maths unit - 3 book back answer

Draw the parabola by the plotting the points (-4, 12), (-3, 6), (-2, 2), (-1, 0), (0, 0), (1, 2), (2, 6), (3, 12), (4, 20), (5, 30)
10th maths unit - 3 book back answer

To solve: x2 + 1 = 0, subtract x2 + 1 = 0 from y = x2 + x.
x2 + 1 = 0 from y = x2 + x
10th maths unit - 3 book back answer

Plotting the points (-2, -3), (0, -1), (2, 1) we get a straight line. This line does not intersect the parabola. Therefore there is no real roots for the equation x2 + 1 = 0.

4. Draw the graph of y = x2 + 3x + 2 and use it to solve x2 + 2x + 1 = 0.
Solution:
10th maths unit - 3 book back answer

Draw the parabola by plotting the point (-4, 6), (-3, 2), (-2, 0), (-1, 0), (0, 2), (1, 6), (2, 12), (3, 20), (4, 30).

10th maths unit - 3 book back answer

To solve x2 + 2x + 1 = 0, subtract x2 + 2x + 1 = 0 from y = x2 + 3x + 2
10th maths unit - 3 book back answer

Draw the straight line by plotting the points (-2, -1), (0, 1), (2, 3)
The straight line touches the parabola at the point (-1,0)
Therefore the x coordinate -1 is the only solution of the given equation





5. Draw the graph of y = x2 + 3x – 4 and hence use it to solve x2 + 3x – 4 = 0. y = x2 + 3x – 4
Solution:

10th maths unit - 3 book back answer

Draw the parabola using the points (-4, 0), (-3, -4), (-2, -6), (-1, -6), (0, -4), (1, 0), (2, 6), (3, 14), (4, 24).
10th maths unit - 3 book back answer

To solve: x2 + 3x – 4 = 0 subtract x2 + 3x – 4 = 0 from y = x2 + 3x – 4 ,
10th maths unit - 3 book back answer

The points of intersection of the parabola with the x axis are the points (-4, 0) and (1, 0), whose x – co-ordinates (-4, 1) is the solution, set for the equation x2 + 3x – 4 = 0.

6. Draw the graph of y = x2 – 5x – 6 and hence solve x2 – 5x – 14 = 0.
Solution:

10th maths unit - 3 book back answer

Draw the parabola using the points (-5, 44), (-4, 30), (-3, 18), (-2, 8), (-1, 0), (0, -6), (1, -10), (2, -12), (3, -12), (4, -10)
10th maths unit - 3 book back answer

To solve the equation x2 – 5x – 14 = 0, subtract x2 – 5x – 14 = 0 from y = x2 – 5x – 6.
10th maths unit - 3 book back answer

The co-ordinates of the points of intersection of the line and the parabola forms the solution set for the equation x2 – 5x – 14 = 0.
∴ Solution {-2, 7}

7. Draw the graph of y = 2x2 – 3x – 5 and hence solve 2x2 – 4x – 6 = 0. y = 2x2 – 3x – 5
Solution:
10th maths unit - 3 book back answer

Draw the parabola using the points (-4, 39), (-3, 22), (-2, 9), (-1, 0), (0, -5), (1, -6), (2, -3), (3, 4), (4, 15).
10th maths unit - 3 book back

To solve 2x2 – 4x – 6 = 0, subtract it from y = 2x2 – 3x – 5
10th maths unit - 3 book back answer

Draw a straight line using the points (-2, -1), (0, 1), (2, 3). The points of intersection of the parabola and the straight line forms the roots of the equation.
The x-coordinates of the points of intersection forms the solution set.
∴ Solution {-1, 3}

8. Draw the graph of y = (x – 1)(x + 3) and hence solve x2 – x – 6 = 0.
Solution:
y = (x – 1)(x + 3) = x2 – x + 3x – 3 = 0
y = x2 + 2x – 3
10th maths unit - 3 book back answer

Draw the parabola using the points (-4, 5), (-3, 0), (-2, -3), (-1,-4), (0, -3), (1, 0), (2, 5), (3, 12), (4, 21)

10th maths unit - 3 book back answer

To solve the equation x2 – x – 6 = 0, subtract x2 – x – 6 = 0 from y = x2 – 2x – 3.
10th maths unit - 3 book back answer

Plotting the points (-2, -3), (-1, 0), (0, 3), (2, 9), we get a straight line.
The points of intersection of the parabola with the straight line give the roots of the equation. The co¬ordinates of the points of intersection form the solution set.
∴ Solution {-2, 3}

Other Important Links for 10th Maths Book Back Answers Solutions:

For 10th Maths Chapter 3 book back question and answers, check the link – Samacheer kalvi 10th Maths Chapter 3 Algebra

Click here for the complete Samacheer Kalvi 10th Maths Book Back Solution Guide PDF – 10th Maths Book Back Answers



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