Question

If a and b are non-zero distinct roots of x² + ax + b = 0, then the least value of  x² + ax + b is

(a)  2/3

(b)  9/4

(c)   -9/4

(d)   1

Answer 1

Correct option  (c) -9/4

a and b are roots of x² + ax + b = 0.

Sum of roots: a + b = −a, 2a + b = 0

Product of roots: ab = b,b(a - 1) = 0

Minimum value of x² + ax + b at x = -a/2 = -1/2

= 1/4 + (-1/2) - 2 = -9/4