Question

If x-2 is factor of polynomial 5x²+mx, then value of m is​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{(x-2)\;is\;a\;factor\;of\;5x^2+mx}$

$\underline{\textbf{To find:}}$

$\textsf{The value of m}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Concept used:}}$

$\boxed{\textbf{(x-a) is a factor of P(x) if and nly if P(a)=0}}$

$\mathsf{P(x)=5x^2+mx}$

$\textsf{Since (x-2) is a factor of P(x), we have P(2)=0}$

$\implies\mathsf{5(2)^2+m(2)=0}$

$\implies\mathsf{5(4)+2m=0}$

$\implies\mathsf{20+2m=0}$

$\implies\mathsf{2m=-20}$

$\implies\mathsf{m=\dfrac{-20}{2}}$

$\implies\boxed{\mathsf{m=-10}}$

$\underline{\textbf{Find more:}}$

Verify whether (x + 1), (x – 2) and (x + 3) are the factors of the polynomial x3 + 2x2– 5x – 6 without actual

division. with the explanation

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