Question

if -5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation
p(x² + x) + k = 0 has equal roots, find the value of k.

Answer 1

Answer:

-1/2

Step-by-step explanation:

if -5 is a root of this equation then will satisfy this equation.

2(-5^2)-5p-15=0

50-15=5p

so, p=7

px^2+px+k=0

let t is the root of this equation.

7x^2+7x+k=0

we know its has equal roots.if one root is t then other is also t.

so,

sum of the roots=-b/a

t+t=-7/7

2t=-1

t=-1/2

product of the roots=c/a

t×t=k/7

1/4=k/7

so, k=7/4 ans