Mathematics

# Quadratic Equations Exercise 9.10 – Class X

I.Solve the following equations graphically.

(i) x2 – 4x = 0

(ii) x2 + x – 12 = 0

(iii) x2 – x – 2 = 0

(iv) x2 – 5x + 6 = 0

II.

1. Draw the graph of y = x2 and find the value of √3
2. Draw the graph of y = 2x2 and find the value of √7
3. Draw the graph of y = 1/2y2 and find the value of √10

## Quadratic Equations – Exercise 9.10 – Solutions:

I.Solve the following equations graphically.

(i) x2 – 4x = 0

Solution:

Prepare the table of the values for the equation y = x2 – 4x

 x -1 0 1 2 3 4 5 y 5 0 -3 -4 -3 0 5 The parabola intersects the x – axis at (0, 0) and (4, 0)

Therefore, the roots of equation are 0 and 4.

(ii) x2 + x – 12 = 0

Solution:

Prepare the table of the values for the equation  x2 + x – 12 = 0

 x -4 -3 -2 -1 0 1 2 3 4 y 0 6 -10 -12 -12 -10 -6 0 8 The parabola intersects the x – axis only at (3, 0) and (-4, 0)

Therefore, the roots of equation are 3 and -4.

(iii) x2 – x – 2 = 0

Solution:

Prepare the table of the values for the equation  x2 – x – 2 = 0

 x -2 -1 0 1 2 3 y 4 0 -2 -2 0 4 The parabola intersects the x – axis at (-1, 0) and (2, 0)

Therefore, the roots of equation are -1 and 2.

(iv) x2 – 5x + 6 = 0

Solution:

Prepare the table of the values for the equation y = x2 – 5x + 6

 x 0 1 2 3 4 5 y 6 2 0 0 2 6 The parabola intersects the x – axis at (2, 0) and (3, 0)

Therefore, the roots of equation are 2 and 3.

II.

1. Draw the graph of y = x2 and find the value of √3

Solution:

y = x2

 x 0 -1 1 -2 2 √3 y 0 1 1 4 4 3 When x = √3, y = (√3)2 = 3

Draw a straight line y = 3 parallel to x-axis

The point on x – axis at which the perpendiculars meets are the values of √3 , x = ±1.7

Therefore, √3 = ±1.7

1. Draw the graph of y = 2x2 and find the value of √7

Solution:

y = 2x2

 x 0 -1 1 -2 2 -3 3 √7 y 0 2 2 8 8 18 18 14 When x = √7, y = 2(√7)2 = 14

Draw a straight line y = 14 parallel to x-axis.

The point on x – axis at which the perpendiculars meets are the values of √7 , x = ±2.6

Therefore, √7 = ±2.6

1. Draw the graph of y = 1/2x2 and find the value of √10

Solution:

y = 1/2x2

 x 0 -2 2 -4 4 √10 y 0 2 2 8 8 5 When x = √10, y = 1/2(√10)2 = 5

Draw a straight line y = 5 parallel to x-axis.

The point on x – axis at which the perpendiculars meets are the values of √10 , x = ±3.1

Therefore, √10 = ±3.1