Find the value of a if $2 x^{3} - 6 x^{2} + 5 a x - 9$ leaves the remainder 13 when it is divided by x-2.

Open in App

Solution

Let $p (x) = 2 x^{3} - 6 x^{2} + 5 a x - 9$
When p(x) is divided by (x -2) the remainder is p(2).
Given that p(2)=13
$\to 2 (2)^{3} - 6 (2)^{2} + 5 a (2) - 9 = 13$
$2 (8) - 6 (4) + 10 a - 9 = 13$
$16 - 24 + 10 a - 9 = 13$
$10 a - 17 = 13$
$10 a = 30$
$∴ a = 3$

Suggest Corrections

Similar questions

6 x^{2} + 5 a x - 12 a

x^{3} - 6 x^{2} + m x + 60

(x + 2)

If the polynomials $a x^{3} + 3 x^{2}$ - 13 and $2 x^{3}$ - 5x + a, when divided by (x-2), leave the same remainders, find the value of a.

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

Join BYJU'S Learning Program