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. OR (c) If the zeroes of the polynomial are −5 and 3, find its expression.

 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