Question

6$x^2$ + ax + 7 when divided by x-2 gives remainder 13. Find the value of a.

Answer 1

Let p(x) = 6$x^2$ + ax + 7.

According to remainder theorem, if (x-2) divides p(x) and remainder is 13 then, p(2) = 13

p(2) = 6${\left(2\right)}^2$ + a(2) + 7 = 13

⇒ 24 + 2a + 7 = 13

⇒ 2a = -24-7+13 = -18

⇒ a = -9