Question

if -5 is Q root of the quadratic equation 2x^+px-15-0 and the quadratic equation p(x^+x+k=0. has equal roots find the value of k​

Answer 1

Answer:

if -5 is Q root of the quadratic equation 2$x^{2}$+p$x$-15=0 and the quadratic equation p$x^{2}$+$x$+k=0 has equal roots then the value of k​ will be 1/4.

Step-by-step explanation:

If -5 is Quadratic root of the quadratic equation 2$x^{2}$+p$x$-15=0, then

$2.(-5)^{2}+p(-5)-15=0$

⇒  $20-5p-15=0$

⇒ $5p=5$

⇒ $p=1$

and the quadratic equation p$x^{2}$+$x$+k=0 has equal roots

∴ $b^{2}-4ac=0$

⇒ $1-4pk=0$

⇒ $1-4(1)k= 0 [since p=1]$

⇒ $1-4k=0$

⇒ $4k=1$

⇒ $k=\frac{1}{4}$

Therefore, the value of k will $k=\frac{1}{4}$ .