Question

If x be real and the roots of the equation ax² + bx + c = 0 are imaginary, then the expression a²x + abx + ac  is always

(A)  Positive 

(B)  Negative 

(C)  Non-positive 

(D)  Non-negative 

Answer 1

Correct option  (A) Positive 

ax² + bx + c = 0 has imaginary roots. That is b² - 4ac <0

The discriminate of the equation f(x) = a²x² + abx + ac is

D = a²b² - 4a²ac = a²(b² - 4ac) < 0

The coefficient of x² in quadratic equation is (a² > 0) positive. That is, a²x² + abx + ac > 0.