Question

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.

Options

• x² + 4 = 0

• x² − 4 = 0

• 4x² − 1 = 0

• x² − 2 = 0

Answer 1

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is x² − 4 = 0.

Explanation:

Let α and β be the roots of quadratic equation in such a way that a = 2

Then, according to question sum of the roots

α + β = 0

2 + β = 0

β = – 2

And the product of the roots

α . β = 2 × (– 2)

= – 4 

As we know that the quadratic equation

x² – (α + β) x + αβ = 0

Putting the value of α and β in above

Therefore, the require equation be

x² − 0 × x + (− 4) = 0

x² − 4 = 0