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Question: Answered & Verified by Expert
If $b^{2} \geq 4 a c$ for the equation $a x^{4}+b x^{2}+c=0$, then all the roots of the equation will be real if
MathematicsSequences and SeriesVITEEEVITEEE 2007
Options:
  • A $b>0, a < 0, c>0$
  • B $b < 0, a>0, c>0$
  • C $b>0, a>0, c>0$
  • D $b>0, a>0, c < 0$
Solution:
2377 Upvotes Verified Answer
The correct answer is: $b>0, a>0, c>0$
Given: $a x^{4}+b x^{2}+c=0$
$\begin{array}{l}
\text { Equation will be real if } \mathrm{D} \geq 0 \\
\Rightarrow \mathrm{b}^{2}-4 \mathrm{ac} \geq 0 \Rightarrow \mathrm{b}^{2} \geq 4 \mathrm{ac}
\end{array}$

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