Question

If -5 is a root of the quadratic equation 2x² + px - 15 = 0 and the quadratic equation
p (x² + x) + k = 0 has equal roots, find the value of k.
(CBSE 2014)​

Answer 1

Answer:

1.75

Step-by-step explanation:

Given,

'-5' is the root of the quadratic equation '2x² + px - 15 = 0 '.

p (x² + x) + k = 0 has equal roots.

To Find :-

Value of 'k'

How To Do :-

As '-5' is the root of the equation , -5 satisfies the value of 'x' in the equation. So by substituting the value of we will get the value of 'p'. After  finding the value of 'p' we need to substitute it the another equation. as they said that the equation has both roots are equal we can apply the formula of discriminant and equate it zero.

Formula Required :-

If 'ax² + bx + c = 0' is the general form of quadratic equation , then the discriminant (D) is :-

Δ = b² - 4ac

Solution :-

Substituting '-'5 in place of x :-

2(-5)² + p(-5) - 15 = 0

2(25) - 5p - 15 = 0

50 - 15 - 5p = 0

35 - 5p = 0

35 = 5p

35/5 = p

p = 7

∴ Value of 'p' = 7

p(x² + x) + k = 0

7(x² + x) + k = 0

7x² + 7x + k = 0

Δ = 0 [ Since equal roots]

Comparing '7x² + 7x + k = 0' with general form of quadratic equation 'ax² + bx + c = 0'

→ a = 7 , b = 7 , c = k

Δ = b² - 4ac

0 = (7)² - 4(7)(k)

0 = 49 - 28k

28k = 49

k = 49/28

k = 1.75

∴ Value of 'k'  = 1.75