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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 $p(x) = -0.0025x^2 - 0.025x + 136$.
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
(iii) (b) Find the values of $p(x)$ at $x = 100$ and $x = -100$. Are they same?
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
(iii) (b) Find the values of $p(x)$ at $x = 100$ and $x = -100$. Are they same?
Show SolutionHide Solution↓
Sol. (i) At $x = 0, p(x) = 136$
Coordinates of point A = $(0,136)$ (I Mark)
(ii) Span of the arch = $238.5 + 228.5 = 467$ units (I Mark)
(iii) (a) Zeroes of the polynomial are $228.5$ and $-238.5$ (I Mark)
Sum of zeroes = $-10 = \frac{-0.025}{-0.0025} = \frac{\text{coefficient of } x}{\text{coefficient of } x^2}$ (II Mark)
OR
(iii) (b) $p(100) = 108.5$ (I Mark)
$p(-100) = 113.5$ (II Mark)
$\therefore p(100) \neq p(-100)$ (III Mark)
Coordinates of point A = $(0,136)$ (I Mark)
(ii) Span of the arch = $238.5 + 228.5 = 467$ units (I Mark)
(iii) (a) Zeroes of the polynomial are $228.5$ and $-238.5$ (I Mark)
Sum of zeroes = $-10 = \frac{-0.025}{-0.0025} = \frac{\text{coefficient of } x}{\text{coefficient of } x^2}$ (II Mark)
OR
(iii) (b) $p(100) = 108.5$ (I Mark)
$p(-100) = 113.5$ (II Mark)
$\therefore p(100) \neq p(-100)$ (III Mark)