Practice Set 2.5
- Activity: Fill in the gaps and complete. (1) (2) = - 7 angle angle (3) If α, β are…
- x^2 + 7x - 1 = 0 Find the value of discriminant.
- 2y^2 - 5y + 10 = 0 Find the value of discriminant.
- root 2x^2 + 4x+2 root 2 = 0 Find the value of discriminant.
- x^2 - 4x + 4 = 0 Determine the nature of roots of the following quadratic equation.…
- 2y^2 - 7y + 2 = 0 Determine the nature of roots of the following quadratic equation.…
- m^2 + 2m + 9 = 0 Determine the nature of roots of the following quadratic equation.…
- Form the quadratic equation from the roots given below. (1) 0 and 4 (2) 3 and -10 (3)…
- Sum of the roots of a quadratic equation is double their product. Find k if equation is…
- α, β are roots of y^2 - 2y - 7 = 0 find, (1) α^2 + β^2 (2) α^3 + β^3…
- 3y^2 + ky + 12 = 0 The roots of each of the following quadratic equation are real and…
- kx (x-2) + 6 = 0 The roots of each of the following quadratic equation are real and…
Practice Set 2.5
Question 1.
Activity: Fill in the gaps and complete.
(1) 
(2) 
(3) If α, β are roots of quadratic equation,
Answer:
(1) Roots are distinct and real when b2 - 4ac = 5, not real when b2 - 4ac = -5.
(2) x2 + 7x + 5 = 0
(3) 
Question 2.
Find the value of discriminant.
x2 + 7x – 1 = 0
Answer:
⇒ 
⇒ 
Question 3.
Find the value of discriminant.
2y2 – 5y + 10 = 0
Answer:
⇒ 
⇒ 
Question 4.
Find the value of discriminant.
Answer:
⇒ 
⇒ 
Question 5.
Determine the nature of roots of the following quadratic equation.
x2 – 4x + 4 = 0
Answer:
⇒ 
⇒ 
∴ 
Question 6.
Determine the nature of roots of the following quadratic equation.
2y2 – 7y + 2 = 0
Answer:
⇒ 
⇒ 
∴ 
Question 7.
Determine the nature of roots of the following quadratic equation.
m2 + 2m + 9 = 0
Answer:
⇒ 
⇒ 
∴ 
Question 8.
Form the quadratic equation from the roots given below.
(1) 0 and 4
(2) 3 and -10
(3) 
(4) 
Answer:
(1) Let 
∴ 
∴
∴ 
∴ 
(2) Let 
∴ 
∴
∴ 
∴ 
(3) Let 
∴ 
∴
∴ 
∴ 
∴ 
(4) Let 
∴ 
∴
∴ 
∴ 
Question 9.
Sum of the roots of a quadratic equation is double their product. Find k if equation is
x2 – 4kx + k + 3 = 0
Answer:
According to question
⇒ 
⇒ 
⇒ 
Question 10.
α, β are roots of y2 – 2y – 7 = 0 find,
(1) α2 + β2
(2) α3 + β3
Answer:
(1). 
⇒ 
⇒ 
⇒ 
(2). 
⇒ 
⇒ 
⇒ 
Question 11.
The roots of each of the following quadratic equation are real and equal, find k.
3y2 + ky + 12 = 0
Answer:
⇒ 
⇒ 
∴ 
⇒ 
⇒ 
∴ 
Question 12.
The roots of each of the following quadratic equation are real and equal, find k.
kx (x-2) + 6 = 0
Answer:
⇒ 
⇒ 
∴
⇒ 
⇒ 
∴ 
