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Mathematics · 2026 · 4 marks
CBSE 2026 · Region 5 · Set 1 · Q36
An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills at P and Q. If the…
An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills at P and Q. If the parabolic curve is represented by the polynomial $\displaystyle \mathrm{p}(x)=-0.0025 x^{2}-$ $\displaystyle 0.025 x+136$. Observe the diagram and based on above information, answer the following questions :
(i)
Write the co-ordinates of point A.
(ii)
Find the span of the arch.
(iii)
(a)
Write the zeroes of the polynomial using diagram and verify the relationship between sum of zeroes and polynomials.
OR
(b)
Find the values of $\displaystyle \mathrm{p}(x)$ at $\displaystyle x=100$ and $\displaystyle x=-100$. Are they same ?
Marking-scheme solution
(i) At \(\displaystyle \mathrm{x}=0, \mathrm{p}(\mathrm{x})=136\)
∴ Coordinates of point \(\displaystyle A=(0,136)\)
(ii) Span of the arch \(\displaystyle =238.5+228.5=467\) units
(iii) (a) Zeroes of the polynomial are $\displaystyle 228.5$ and - $\displaystyle 238.5$
Sum of zeroes \(\displaystyle =-10=-\frac{-0.025}{-0.0025}=-\frac{\text { coefficient of } \mathrm{x}}{\text { coefficient of } \mathrm{x}^{2}}\) OR(iii) (b) \(\displaystyle \mathrm{p}(100)=108.5\)
\(\displaystyle \mathrm{p}(-100)=113.5\)
\(\displaystyle \therefore \mathrm{p}(100) \neq \mathrm{p}(-100)\)
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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.