Question

If -5 is a root of quadratic equation 2x^+px-15=0 and quadratic equation px^+4px+k=0 has equal roots find k

Answer 1

Answer:

K=28

Step-by-step explanation:

$2 {x}^{2} + px - 15 = 0 \\ 2 {( - 5)}^{2} + p( - 5) - 15 = 0 \\ 2(25) - 5p - 15 = 0 \\ 50 - 5p - 15 = 0 \\ 35 - 5p = 0 \\ - 5p = - 35 \\ p = 7 \\ p {x}^{2} + 4px + k = 0 \\ 7 {x}^{2} + 28x + k = 0 \\ a = 7 \\ b = 28 \\ c = k \\ d = {b}^{2} - 4ac \\ 0 = {(28)}^{2} - 4(7)(k) \\ 0 = 784 - 28k \\ 784 = 28k \\ k = 28$