Question

find all the zeroes of the
polynomial
${x}^{3} + 3 {x}^{2} - 2x - 6$

if two of its zeroes are 0 and -2​

Answer 1

$\huge\boxed{\fcolorbox{blue}{orange}{HELLO\:MATE}}$

GIVEN:

→${x}^{3} + 3 {x}^{2} - 2x - 6$

→Two of it's zeroes are 0 and -2.

TO FIND:

→All zeroes of the polynomial.

ANSWER:

Let p(x) = ${x}^{3} + 3 {x}^{2} - 2x - 6$

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We would find it's zeroes by the method of factorisation and then equating it with 0.

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Let p(x) = 0.

=>${x}^{3} + 3 {x}^{2} - 2x - 6=0$

=>$x^{2}(x+3) -2(x+3) =0$

=>$(x^{2}-2) (x+3) =0$

=>${[(x^{2})-(\sqrt{2}) ^{2}]} (x+3) =0$

$\large\green{\boxed{a^{2}-b^{2}=(a+b) (a-b) }}$

=>$(x+\sqrt{2}) (x-\sqrt{2}) (x+3) =0$

=>$x = -3, \sqrt{2}, -\sqrt{2}$

Hence the zeroes are -3, -√2, √2.

$\huge\orange{\boxed{Answer:-3, \sqrt{2}, -\sqrt{2}}}$