Question

Solve the following question

Answer 1

Answer:

k = 7/4.

Step-by-step explanation:

Let f(x) = 2x²+px-15.

If -5 is a root of the above equation, f(-5)=0

i.e 2(-5)² + p(-5) -15 = 0

50 - 15 = 5p

5p = 35

p = 7.

Given another polynomial,

p(x²+x) + k

7x² + 7x + k

Let one of its root be a. Then another root is also a.

Sum of roots, a + a = 2a = -1 ⇒a = -1/2  (-b/a)

Product of roots is a(a) = K/7  (c/a)

1/4 = k/7

∴k = 7/4.