Expression x^3 - 3x^2 - 9x + c can be written in form (x - a)^2 (x - b) if the values of c is

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7.Binomial Theorem

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The expression $x^3 - 3x^2 - 9x + c$ can be written in the form $(x - a)^2 (x - b)$ if the values of $c$ is

A

$-5$ or $27$

B

$5$ or $-27$

C

$5$ or $27$

D

$-5$ or $-27$

Solution

$2 a+b=3, a^{2}+2 a b=-9$

$\Rightarrow a^{2}+2 a(3-2 a)=-9$

$\Rightarrow a^{2}-4 a^{2}+6 a+9=0$

$\Rightarrow-3 a^{2}+6 a+9=0$

$\Rightarrow a^{2}-2 a-3=0$

$\Rightarrow(a+1)(a-3)=0$

$a=-1,3$

$c=-a^{2} b$

$\therefore a=-1, b=5;$

$a=3, b=-3$

$\therefore c=-5$ or $27$

Standard 11

Mathematics

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