Question

. If -5 is a root of 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

Given

-5 is a root of quadratic equation 2x²+px-15=0

and px²+px +k=0 has equal roots .

To Find

we have to find the value of k

$\sf\huge {\underline{\underline{{Solution}}}}$

since , -5 is a root

then it must satisfy the given equation e.g., 2x²+px-15=0

Put -5 into the Equation

=> 2(-5)²+p(-5)-15=0

=> 50+5p-15=0

=> -5p +35=0

=> -5p= -35

=> p= 7

Now, substitute p = 7 in p(x²+x)+k=0

we get,

=> 7(x²+x)+k=0

=>7x²+7x+k=0

Since , the Equation have equal roots

Discriminant = b²-4ac =0

a= 7,b= 7 & c= k

=> (7)²-4(7)(k)=0

=> 49-28k= 0

=> -28k= -49

=>k = -49/-28= 7/4

∴k= 7/4