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  • Find the value of m so that 2x-1 be a factor of 8x^{4}+4x^{3}-16x^{2}+10+m

Find the value of m so that 2x-1  be a factor of 8x^{4}+4x^{3}-16x^{2}+10x+m .

Answers (1)

m=-2

Solution

We know that if (x+a)  is factor of the polynomial f(x), then it always satisfies f(-a)=0

Given, 2x-1  is a factor of 8x^{4}+4x^{3}-16x^{2}+10x+m

Let    p(x)=8x^{4}+4x^{3}-16x^{2}+10x+m

g(x)=2x-1 

According to remainder theorem if g(x) is a factor of p(x) then p\left (\frac{1}{2} \right )=0
\\p\left (\frac{1}{2} \right )=8\left (\frac{1}{2} \right )^{4}+4\left (\frac{1}{2} \right )^{3}-16\left (\frac{1}{2} \right )^{2}+10\left (\frac{1}{2} \right )+m\\ 0=8\times \frac{1}{16}+4\times \frac{1}{8}-16 \times \frac{1}{4}+5+m\\ 0=\frac{1}{2}+\frac{1}{2}-4+5+m\\ 0=1+1+m\\ m=-2

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infoexpert24

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