While playing badminton Ravi has set the barrier chain hung between two posts at the edge of the walkway of a street. It is hung in the shape of a parabola.
Based on the above information answer the following questions :
(a) Which type of the polynomial (linear, quadratic, cubic etc.) is graphically represented by a parabola ?
(b) If the polynomial represented by a parabola, intersects the x-axis at −2 and 3 and y-axis at −3, then write the zeroes of the parabola.
(c) Find the expression for the above polynomial.
(d) If the zeroes of the polynomial are −5 and 3, find its expression.
[a] A parabola is the graph of a quadratic polynomial
Given
parabola, intersects the x-axis at −2 and 3
therefore zeroes are [-2] and 3
Polynomial with roots α and β is given by
f(x) = k(x − α)(x − β)
or
f(x) = k[x² − (α + β)x + αβ]
where k ≠ 0 is any real number.
given that zeroes are [-2] and 3
Take them as
α = [-2]
β = 3
f(x) = k(x + 2)(x − 3)
use distribution law
f(x) =k(x² − x − 6)
to find k use the condition that parabola cuts y-axis at −3
which means it passes through (0,-3)
so Use f(0) = −3
k[0-0-6] = [-3]
we get k =(1/2)
and f(x) = (1/2)(x² − x − 6)
in the last part the zeroes are given to be −5 and 3
so g(x) = k(x + 5)(x − 3) =kx² + 2x − 15
choose k=1
g(x) = x² + 2x − 15
see this video for more details
cbse 10th maths old board exam question papers 2025 2026 to find the equation of a polynomial whose zeroes are given
