Question

If p₁ p₂ = 2(q₁ + q₂ ), then at least one of the equations x² + p₁ x + q₁ = 0 and x² + p₂ x + q₂ = 0 has

(1) real roots 

(2) non-real roots 

(3) purely imaginary roots 

(4) none of these

Answer 1

Correct option (1) real roots

Explanation: 

The given equations are

Now, sum of the discriminants

Hence, at least one of the discriminants is non-negative. This implies at least one of the equation has real roots.