Question

If -4 is a root of the quadratic equation x²+px-4=0 ;and the equation 2x²+px+k=0 has equal roots find the value of k

Answer 1

Here given that -4 is a root of x² + px - 4 = 0

∴ x = -4

Putting this value in x² + px - 4 = 0

( -4)²  + p( -4 ) - 4 = 0

16 - 4p - 4 = 0

4p = 12

p = 3 --- ( i )

Now, Given equation 2x² + px + k = 0 has equal roots

∴ Discriminant (D) of the equation = 0

We know that D = (coefficient of x)² - 4 (coefficient of x²)(constant term)

∴ D = p² - 4 × 2 × k = 0 ( ∵ D = 0)

putting value of p from ( i )

9 - 8k = 0

8k = 9

k = 9/8