A quadratic equation whose one root is 2 and the sum of whose roo… - Vidyadip

MCQ

A quadratic equation whose one root is $2$ and the sum of whose roots is zero, is:

A
$x^2 + a^4 = 0$
✓
$x^2 - 4 = 0$
C
$4x^2 - 1 = 0$
D
$x^2 - 2 = 0$

✓

Answer

Correct option: B.

$x^2 - 4 = 0$

Let $\alpha$ and $\beta$ be the roots of quadratic equation in such a way that $\alpha=2$
Then, according to question sum of the roots
$\alpha+\beta=0$
$2+\beta=0$
$\beta=-2$
And the product of the roots
$\alpha\cdot\beta=2\times(-2)$
$\alpha\cdot\beta=-4$
As we know that the quadratic equation
$\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta=0$
Putting the value of $\alpha$ and $\beta$ in above
Therefore, the require be
$\text{x}^2-0\times\text{x}+(-4)=0$
$\text{x}^2-4=0$
Thus, the correct answer is $(b)$

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