Question

if -5 is a root of 2x^2+px-15=0 and roots of p(x^2+x)+k=0are equal then find p and k

Answer 1

2×25-5p-15
=35÷5=p
=7
7(25-5)+k=0
140=-k
-140=k

Answer 2

Answer:

The value of p and k is 7 and -140.

Step-by-step explanation:

$\text{Given that -5 is a root of } 2x^2+px-15=0 \text{ and roots of } p(x^2+x)+k=0 \thinspace and \thinspace 2x^2+px-15=0\text{ are equal }$

we have to find the value of p and k.

As -5 is the root of $2x^2+px-15=0$

⇒ $2(-5)^2+p(-5)-15=0$

⇒ $50-5p-15=0$

35-5p=0 ⇒ p=7

Now, -5 is also the root of $p(x^2+x)+k=0$

⇒ 7(25-5)+k=0

140=-k

-140=k