Question:
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is
(a) $x^{2}+4=0$
(b) $x^{2}-4=0$
(c) $4 x^{2}-1=0$
(d) $x^{2}-2=0$
Solution:
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
$\alpha \cdot \beta=2 \times(-2)$
$=-4$
As we know that the quadratic equation
$x^{2}-(\alpha+\beta) x+\alpha \beta=0$
Putting the value of $\alpha$ and $\beta$ in above
Therefore, the require equation be
$x^{2}-0 \times x+(-4)=0$
$x^{2}-4=0$
Thus, the correct answer is (b)