Question

ax^2 + arx + ar^2 = 0

If a and r are real.

Then roots of the equation are?

a)" "Always imaginary

b)" "Both real roots

c)" "Only one real root

d)" "Depends on r

Solution

Given equation:ax^2 + arx + ar^2 = 0

To check for nature of roots, we need to find the value of discriminant (D).

D = (a^2)(r^2) - 4(a)(ar^2) = a^2(r^2 - 4r^2) = -3(a^2)(r^2)

Hence D will always remain negative.

This proves roots of the equation are always imaginary.