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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
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Verified Answer
The correct answer is:
$b>0, a>0, c>0$
Given: $a x^{4}+b x^{2}+c=0$
$\begin{array}{l}
\text { Equation will be real if } \mathrm{D} \geq 0 \\
\Rightarrow \mathrm{b}^{2}-4 \mathrm{ac} \geq 0 \Rightarrow \mathrm{b}^{2} \geq 4 \mathrm{ac}
\end{array}$
$\begin{array}{l}
\text { Equation will be real if } \mathrm{D} \geq 0 \\
\Rightarrow \mathrm{b}^{2}-4 \mathrm{ac} \geq 0 \Rightarrow \mathrm{b}^{2} \geq 4 \mathrm{ac}
\end{array}$
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