Question

If the equation `ax^(2) + bx + 6 = 0` has real roots, where `a in R, b in R`, then the greatest value of 3a + b, is
A. 4
B. -1
C. -2
D. 1

Answer 1

Correct Answer - C
Let `3a + b = lambda`
Since the equation `ax^(2) + bx + 6 = 0` has real roots.
`therefore" "b^(2) - 24 a ge 0`
`rArr" "b^(2) - 8(lambda - b) ge 0" "[because 3a + b = lambda]`
`rArr" "b^(2)+8b - 8 lambda ge 0` for all b `in` R
`rArr" "64 + 32 lambda le 0 rArr lambda le -2`
Hence, the greatest value of `lambda` is -2.