Question

14. Find the value of k, if x-1 is a factor of p(x) = 5x² + 3x + k​

Answer 1

Answer:

Given :-

x-1 is a factor of p(x) = 5x² + 3x + k​

To find :-

value of k

Solution :-

Let q(x) = x-1

and, p(x) = 5x² + 3x + k​

q(x) = 0 ⇒ x - 1 = 0

             ⇒ x = 1

q(x) is a factor of p(x), so the remainder will be 0.

∴ p(x) = 5x² + 3x + k​

⇒p(1) = 0 ⇒ 5(1)² +3(1) + k = 0

               ⇒ 5(1) + 3 + k = 0

               ⇒ 5 + 3 + k = 0

               ⇒ 8 + k = 0

               ⇒ k = 0 - 8

               ⇒ k = -8

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