Question

if -5 is a root of a quadratic equation 2x² + 3x -15 = 0 and the quadratic equation p(x²+x)+k =0n has equal roots find the value of k​

Answer 1

Answer:

k=0,-2

Step-by-step explanation:

if the quadratic eq. p(x^2+x)+k=0 has equal roots then sum of the two roots=-b/a

=> 2α=-p/p=-1

=> α=-1/2

product=d/a

=> α^2=k/p

=> -1/2=k/p

=> p=-2k

for equal roots,

=> D=0

=> p^2-4pk=0

=> 4k^2-4(-2k) =0

=> 4k^2+8k=0

=> 4k(k+2)=0

=> k=0 or k=-2