CBSE 2025 · Region 1 · Set 2 · Q21 · 2 marks
If the zeroes of the polynomial $\displaystyle \mathrm{x}^{2}+\mathrm{ax}+\mathrm{b}$ are in the ratio $\displaystyle 3$ : $\displaystyle 4$, then prove that $\displaystyle 12 \mathrm{a}^{2}=49 \mathrm{~b}$.
Marking-scheme solution
Let the zeroes are \(\displaystyle 3 \alpha\) and \(\displaystyle 4 \alpha\)
\[\begin{aligned}
& 3 \alpha+4 \alpha=-\mathrm{a} \\
& \Rightarrow 7 \alpha=-\mathrm{a} \\
& \text { Also, } 12 \alpha^{2}=\mathrm{b} \\
& \text { LHS }=12 \mathrm{a}^{2}=12(-7 \alpha)^{2}=49 \times 12(\alpha)^{2}=49 \mathrm{~b}=\text { RHS }
\end{aligned}
\]
PolynomialsRelationship between Zeroes and CoefficientsApplyvery_short_answermedium
More from Polynomials
- Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is:2025 · asked 3×
- If the zeroes of the polynomial a x^2+b x+(2 a)/ are reciprocal of each other, then the value of b is2025 · asked 3×
- Which of the following statements is true for a polynomial p(x) of degree 3?2025 · asked 3×
- If α and β are the zeroes of the polynomial p(x)=x^2-a x-b, then the value of (α+β+α β) is equal to:2025 · asked 2×
- The quadratic equation whose roots are 7 and 1/7 is:2025 · asked 2×
- If α and β are the zeroes of polynomial 3 x^2+6 x+k such that α+β+α β=-2/3, then the value of k is:2025 · asked 2×
- Find the zeroes of the polynomial p(x)=x^2+4/3 x-4/3.2025 · asked 2×
- If p and q are zeroes of the polynomial p(y)=21 y^2-y-2, then find the value of (1-p).(1-q).2025 · asked 2×
CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.