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Find the discriminant of the quadratic polynomial $3\sqrt{3}x^{2}+10x+\sqrt{3}=0$.
Given: Quadratic polynomial $3\sqrt{3}x^{2}+10x+\sqrt{3}=0$.
To do: To find the discriminant of the given quadratic polynomial.
Solution: Given quadratic polynomial is $3\sqrt{3}x^{2}+10x+\sqrt{3}=0$.
On comparing this polynomial to $ax^{2}+bx+c=0$,
we have $a=3\sqrt{3},\ b=10\ and\ c=\sqrt{3}$
Discriminant $D=b^{2}-4ac$
On substituting values of $a,\ b\ and\ c$
$D=10^{2}-4\times3\sqrt{3}\times\sqrt{3}$
$\Rightarrow D=100-36$
$\Rightarrow D=64$
Therefore, the discriminant of the given quadratic polynomial is $64$.
Updated on: 10-Oct-2022
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