Question

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

Answer 1

Answer:

-4 is a root of equation x² + 2x + 4p = 0

=> p(x) = p(-4) = 0

=> (-4)² +2 * (-4) + 4p = 0

=> 16 -8 + 4p = 0

=> 4p = -8

=> p = -2 ………………. (1)

Given that quadratic equation

x² - px (1+3k) + 7(3+2k) = 0 has equal roots..

=> discriminant b² - 4ac = 0

=> p²(1+3k)² - 4* 7(3+2k) = 0

Since p = -2

=> 4 ( 1+3k)² - 28 ( 3+2k) = 0

=> 4( 1 + 6k + 9k²) - 84- 56k = 0

=> 4 + 24k + 36k² - 84 - 56k = 0

=> 36k² - 32k - 80 = 0

=> 9k² - 8k - 20 = 0

=> 9k² - 18k +10k -20 = 0

=> 9k(k - 2) + 10(k - 2) =0

=> (k-2) (9k + 10 ) = 0

=> k = 2 & -10/9

Answer 2

Answer:

Refer to the above attachment