Question

if it is been that -1 is one of the zeros of the polynomial x cube + 2 x square - 11 x - 12 find all the zeros of the given polynomial​

Answer 1

Answer:

Given:

-1 is a root of the polynomial  x³+2x²-11x-12

To find:

rest of zeros .

if -1 is a root then p(-1) = 0

⇒ x = -1

or,  x+1 =0

⇒ (x+1) is a factor of the given polynomial.

let's divide with this.

$\begin{array}{c|c}nothi&x^2+x-12\cline{2-3}(x+1)&x^3+2x^2-11x-12\cline{2-3}-&-(x^3+x^2)\cline{2-3}-&x^2-11x-12\cline{2-3}-&-(x^2+x)\cline{2-3}-&-12x-12\cline{2-3}-&-(-12x-12)\cline{2-3}-&0\end{array}$

Thus, we get quotient as

x²+x-12

quadratic equation  -b±√b²-4ac/2a

$substitute \\\\ \dfrac{-1 \pm \sqrt{1-4(-12)(1)}}{2}\\\\\implies \dfrac{-1 \pm \sqrt{49}}{2}\\\\\implies \dfrac{-1 \pm7}{2}\\\\\implies \boxed{ x =3\:or \:-4}$

Thus, the remaining zeros are 3 and -4