✓ Board-verified
Mathematics · 2026 · 4 marks
CBSE 2026 · Region 3 · Set 1 · Q36
During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the polynomial p ( x )=-…
During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the polynomial $\displaystyle \mathrm{p}(\mathrm{x})=-\mathrm{x}^{2}+2 \mathrm{x}+8$, where x is the length (in feet) on stage level.
Based on the figure given above, answer the following questions :
(i)
Determine the height of the arch.
(ii)
(a)
Find zeroes of the polynomial p(x). Which points on the graph represent the zeroes ?
OR
(b)
Find the span of the arch on the stage floor.
(iii)
Write the coordinates of the point of intersection of the above curve with the y -axis.
Marking-scheme solution
(i)
$\displaystyle p(1)=-(1)^{2}+2 \times 1+8=9$
So, height of the arch is $\displaystyle 9$ feet.
(ii)
\[\begin{array}{l}
\mathrm{p}(\mathrm{x})=-\mathrm{x}^{2}+2 \mathrm{x}+8 \\
\quad=-(\mathrm{x}-4)(\mathrm{x}+2) \\
\text { zeroes are }-2 \text { and } 4
\end{array}
\]
Points B and A on the graph represent the zeroes.
\[\begin{aligned}
p(x) & =-x^{2}+2 x+8 \\
& =-(x-4)(x+2)
\end{aligned}
\]
∴ zeroes are -$\displaystyle 2$ and 4.
Hence, Coordinates of point A and B are $\displaystyle (4,0)$ and $\displaystyle (-2, 0)$ respectively.
Span of the arch on the stage floor, $\displaystyle \mathrm{AB}=4+2=6$
So, span of the arch on the stage floor is $\displaystyle 6$ feet.
(iii)
$\displaystyle \mathrm{p}(0)=-(0)^{2}+2 \times 0+8=8$
∴ the given curve intersects y-axis at $\displaystyle (0,8)$
More from Polynomials
- A polynomial p(x), which has sum of its zeroes equal to their product, is:2026
- If α, β are the zeroes of the polynomial p(x)=x^2-3 x-1, then find the value of 1/(α)+1/(β).2026
- Find the zeroes of the quadratic polynomial x^2-15 and verify the relationship between the zeroes and the coefficients of the polynomial.2024
- If α, β are zeroes of the polynomial x^2-1, then value of (α+β) is:2023
- 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
- If one zero of the polynomial p(x)=6 x^2+37 x-(k-2) is reciprocal of the other, then find the value of k.2023
- α and β are zeroes of a quadratic polynomial x^2-a x-b. Obtain a quadratic polynomial whose zeroes are 3 α+1 and 3 β+1.2025
- If α and β are the zeroes of the polynomial a x^2-x+c. Obtain a polynomial whose zeroes are α-3 and β-3.2025
CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.