What value should a possess so that x+1 may b | vedclass

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Question

(C) Given the polynomial $f(x) = 2x^{3} - ax^{2} - (2a - 3)x + 2$.According to the Factor Theorem,if $(x + 1)$ is a factor of $f(x)$,then $f(-1) = 0$.

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) Given the polynomial $f(x) = 2x^{3} - ax^{2} - (2a - 3)x + 2$.According to the Factor Theorem,if $(x + 1)$ is a factor of $f(x)$,then $f(-1) = 0$.Substituting $x = -1$ into the polynomial:$f(-1) = 2(-1)^{3} - a(-1)^{2} - (2a - 3)(-1) + 2 = 0$Simplifying the expression:$2(-1) - a(1) + (2a - 3) + 2 = 0$$-2 - a + 2a - 3 + 2 = 0$Combining like terms:$a - 3 = 0$$a = 3$Therefore,the value of $a$ is $3$.

What value should $a$ possess so that $x+1$ may be a factor of the polynomial $f(x)=2x^{3}-ax^{2}-(2a-3)x+2$?

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