Question

If x1, x2 are real roots of ax^2 – x + a = 0. Then, find the set of all values of parameter ‘a’ for which |x1 – x1| < 1?

(a) (1 – 5a)/ a^2 < 0

(b) (1 – 5a)/ a^2 = 0

(c) (1 – 5a)/ a^2 > 0

(d) (1 – 5a)/ a < 0

I have been asked this question during an online interview.

My question is from Applications of Quadratic Equations topic in portion Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

Correct choice is (a) (1 – 5a)/ a^2 < 0

The explanation is: |x1 – x2| < 1

 = (x1 – x2)^2 < 1

= (x1 + x2)^2 – 4 x1 x2 -1 < 0

= (1/a)^2 – 4 – 1 < 0

= (1 – 5a)/a^2 < 0.