A quadratic equation whose one root is 2 and
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)

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