Practice Set 2.1 Quadratic Equations Class 10th Mathematics Part 1 MHB Solution

Practice Set 2.1

1. Write any two quadratic equations.
2. Decide which of the following are quadratic equations. (1) x^2 + 5x - 2 = 0 (2) y^2 =…
3. Write the following equations in the form ax^2 + bx + c = 0, then write the values of…
4. Determine whether the values given against each of the quadratic equation are the roots…
5. Find k if x = 3 is a root of equation kx^2 - 10x + 3 = 0.
6. 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.

⇒ 

⇒ 

⇒ 

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