Question

The equation $a{x}^2+bx+c$ = 0 does not have real roots and c < 0. Which of these is true?

• A. b > a + c
• B. 4a + 2b + c < 0
• C. a + b + c > 0
• D. Both (a) & (b)

Answer 1

The correct option is D

Both (a) & (b)

Given equations does not have any real roots

D < 0 $\Rightarrow b^2-4ac<0$

$b^2<4ac$

$4ac>b^2$

4ac > 0 [As $b^2>0$]

ac > 0

As c < 0, 'a' must be -ve for ac > 0

So, a < 0 & D < 0 $\Rightarrow$ Graph is downward & does not touch x-axis

So, f(x) < 0

f(-1) = a - b + c < 0 $\Rightarrow$ b > a + c

f(2) = 4a +2b + c < 0

so, both options a & b are true