Question

If b$^2 \ge 4 ac$ for the equation $ax^4 + bx^2 + c = 0$, then all the roots of the equation will be real if

• A. b>0, a<0, c>0
• B. b<0, a>0, c>0
• C. b>0, a>0, c>0
• D. b>0, a>0, c<0

Answer 1

Answer: (C)

Given : $ax^4 + bx^2 + c + 0$
Equation will be real if D $\ge$ 0
$\Rightarrow b^2 - 4ac \ge 0 \Rightarrow b^2 \ge 4ac$