(D) Let $f(x) = x^5-6x^4+11x^3-2x^2-12x+8$. By testing small integer roots,we find that $x=2$ is a root. Using synthetic division or polynomial divisi

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(D) Let $f(x) = x^5-6x^4+11x^3-2x^2-12x+8$. By testing small integer roots,we find that $x=2$ is a root. Using synthetic division or polynomial division,we factor the expression: $f(x) = (x-2)^3(x^2-1) = (x-2)^3(x-1)(x+1)$. The roots are $x=2$ (with multiplicity $3$),$x=1$,and $x=-1$. Since $\alpha$ is a multiple root,$\alpha=2$. Substituting $\alpha=2$ into the expression $3\alpha^2-2\alpha+1$: $3(2)^2-2(2)+1 = 3(4)-4+1 = 12-4+1 = 9$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

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If $\alpha$ is a multiple root of the equation $x^5-6x^4+11x^3-2x^2-12x+8=0$,then $3\alpha^2-2\alpha+1=$

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A
-$2$
B
$1$
C
$0$
D
$9$

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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