Question

If the polynomial 6x4+8x3-5x2+ax+b is exactly divisible by the polynomial 2x2-5, then find the value of a and b.

Answer 1

Answer:

ab square is the answer

Answer 2

a = -20 and b = -25

Step-by-step explanation:

The given polynomial $6x^{4}+8x^{3}-5x^{2}+ax+b$ (say $p(x)$ ) is exactly divisible by the polynomial $2x^{2}-5$ (say q(x) )

This implies that, p(x), when divided by q(x), gives a remainder of 0.

So, lets divide $p(x)= 6x^{4}+8x^{3}-5x^{2}+ax+b$

by $q(x) = 2x^{2}-5$

We get remainder, $r(x) = (20+a)x+25+b$

but $r(x)=0$ (According to the given condition)

So, $(20+a)x+25+b = 0$

$\Rightarrow (20+a)x+25+b = 0 \cdot x +0\\\Rightarrow 20+a=0 \ \& \ 25+b=0\\\Rightarrow \ \ \ a=-20\ \& \ b=-25$

Thus, a = -20, b = -25.