Question

If x = - 4 is a root of the equation x square + 2x + 4p = 0 , find the values of K for which the equation x square + px(1 + 3k) + 7(3 + 2k) = 0 has equal roots.

Answer 1

the value of p=_2or the value of k=_45÷38

Answer 2

Substitute the value of x = -4 in the 1st equation
=> 16 - 8 + 4p = 0
=> p = -2 --------(1)

Now put (1) in the 2nd equation given in the question,

x^2 + px(1+3k) + 7(3+2k) = 0

as the roots are equal, discriminant will be equal to 0.

OR

D = 0
b^2 - 4ac = 0
[-2(1+3k)]^2 - 4[7(3+2k)] = 0

4[1+3k]^2 = 4[7(3+2k)]

[1+3k]^2 = [7(3+2k)]

1 + 9k^2 + 6k = 21 + 14k

9k^2 - 8k - 20 = 0

on solving we'll get k = 2 or k = -10/9 ;)