- Write any two quadratic equations.
- Decide which of the following are quadratic equations. (1) x^2 + 5x - 2 = 0 (2) y^2 =…
- Write the following equations in the form ax^2 + bx + c = 0, then write the values of…
- Determine whether the values given against each of the quadratic equation are the roots…
- Find k if x = 3 is a root of equation kx^2 - 10x + 3 = 0.
- One of the roots of equation 5m^2 + 2m + k = 0 is -7/5 Complete the following activity…

###### Practice Set 2.1

Question 1.Write any two quadratic equations.

Answer:

and

Question 2.

Decide which of the following are quadratic equations.

(1) x2 + 5x – 2 = 0

(2) y2 = 5y - 10

(3)

(4)

(5) (m + 2)(m–5) = 0

(6) m3 + 3m2 – 2 = 3 m3

Answer:

1. is a quadractic equation because it is the form of and it has degree 2.

2.

∴ it is a quadratic equation because it is the form of and it has degree 2.

3.

⇒

∴ it is not a quadratic equation because it is not in the form of and it does not have degree 2.

4.

∴ it is a quadratic equation because it is the form of and it has degree 2.

5.

⇒

∴ it is a quadratic equation because it is the form of and it has degree 2.

6.

⇒

∴ it is not a quadratic equation because it is not in the form of and it does not have degree 2.

Question 3.

Write the following equations in the form ax2 + bx + c = 0, then write the values of a, b, c for each equation.

(1) 2y = 10 – y2

(2) (x-1)2 = 2x + 3

(3) x2 + 5x = - (3-x)

(4) 3m2 = 2m2 - 9

(5) P(3 + 6p) = - 5

(6) x2 – 9 = 13

Answer:

(1)

⇒

y2 + 2y - 10 = 0;

a = 1, b = 2, c = -10

(2)

⇒

⇒

⇒ x2 - 4x - 2 = 0;

a = 1, b = -4, c = -2

(3) ⇒

⇒

⇒ x2 + 4x + 3 = 0;

a = 1, b = 4, c = 3

(4) ⇒

a = 1, b = 0, c = 9

(5) ⇒

;

a = 6, b = 3, c = 5

(6) ⇒

= 0

a = 1, b = 0, c = -22

Question 4.

Determine whether the values given against each of the quadratic equation are the roots of the equation.

(1) x2 + 4x – 5 = 0, x = 1, -1

(2)

Answer:

1)

Put

⇒

⇒

Put

⇒

⇒

∴ is a root of the equation and is not a root of the equation.

2)

Put , ⇒ ⇒

Put , ⇒

∴ is not root of the equation and is a root of the equation.

Question 5.

Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.

Answer:

Put

⇒

⇒

⇒

⇒

⇒

Question 6.

One of the roots of equation 5m2 + 2m + k = 0 is Complete the following activity to find the value of 'k'.

Answer:

is a root of quadratic equation

∴ Put in the equation.

⇒

⇒

⇒

7