Question

if polynomial q(t) = 4t³+3t²+t-2a multiple of 2t-1 ?​

Answer 1

Explanation:

If 2t - 1 is a factor of q(t), then its zero, 1/2, when substituted with t in q(t), will make its value zero. Such is said by the Factor Theorem.

$\mathsf{q(\frac{1}{2})=4(\frac{1}{2})^3+3(\frac{1}{2})^2+\frac{1}{2}-2a}$

$\mathsf{=\frac{1}{2}+\frac{3}{4}+\frac{1}{2}-2a}$

$\mathsf{=\frac{2+3+2-8a}{4}=\frac{7-8a}{4}}$

However, we know that q(1/2) has to be 0.

∴ $\mathsf{\frac{7-8a}{4}=0}$

$\mathsf{==>7-8a=0}$

$\mathsf{==>-8a=-7}$

∴ $\mathsf{a=\frac{-7}{-8}=\frac{7}{8}}$

Answer: a = 7/8

I hope this helps. :D