The zeros of the polynomial x^2- 2x-12 are : - Vidyadip

MCQ

The zeros of the polynomial $\text{x}^2-\sqrt2\text{x}-12$ are :

A
$\sqrt2,\ -\sqrt2$
✓
$3\sqrt2,\ -2\sqrt2$
C
$-3\sqrt2,\ 2\sqrt2$
D
$3\sqrt2,\ 2\sqrt2$

✓

Answer

Correct option: B.

$3\sqrt2,\ -2\sqrt2$

$\text{f}(\text{x})=\text{x}^2-\sqrt2\text{x}-12$
$=\text{x}^2-3\sqrt2\text{x}+2\sqrt2\text{x}-12$
$=\text{x}\big(\text{x}-3\sqrt2\big)+2\sqrt2\big(\text{x}-3\sqrt2\big)$
$=\big(\text{x}-3\sqrt2\big)\big(\text{x}+2\sqrt2\big)$
$\therefore\text{f}(\text{x})=0$
$\Rightarrow\big(\text{x}-3\sqrt2\big)\big(\text{x}+2\sqrt2\big)=0$
$\Rightarrow\text{x}-3\sqrt2=0$ or $\text{x}+2\sqrt2=0$
$\Rightarrow\text{x}=3\sqrt2$ or $\text{x}=-2\sqrt2$
So, the zeros of given polynomial are $3\sqrt2$ and $-2\sqrt2$

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