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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 4 · Set 1 · Q23
Find the sum and product of the roots of the quadratic equation $\displaystyle 2 \mathrm{x}^{2}-9 \mathrm{x}+4=0$.Find the discriminant of the quadratic equation $\displaystyle 4 \mathrm{x}^{2}-5=0$ and hence comment on the nature of roots of the equation.
Find the sum and product of the roots of the quadratic equation $\displaystyle 2 \mathrm{x}^{2}-9 \mathrm{x}+4=0$.
Find the discriminant of the quadratic equation $\displaystyle 4 \mathrm{x}^{2}-5=0$ and hence comment on the nature of roots of the equation.
Marking-scheme solution
\[\begin{aligned}
& 2 x^{2}-9 x+4=0 \\
& a=2, b=-9, c=4
\end{aligned}
\]
Let \(\displaystyle \alpha, \beta\) be roots of \(\displaystyle 2 \mathrm{x}^{2}-9 \mathrm{x}+4=0\)
\[\begin{aligned}
& \text { Sum }=\alpha+\beta=-\frac{b}{a}=\frac{9}{2} \\
& \text { Product of roots }=\alpha \beta=\frac{c}{a}=\frac{4}{2}=2
\end{aligned}
\]
\[\begin{aligned}
& 4 x^{2}-5=0 \\
& a=4, b=0, c=-5 \\
& \text { Discriminant }=b^{2}-4 a c=0-4(4)(-5)=80>0 \\
& \Rightarrow \text { roots are real and distinct. }
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.