A quadratic polynomial, whose zeroes are -3 and 4, is
a. x2 - x + 12
b. x2 + x + 12
c. x²/2 - x/2 - 6
d. 2x2 + 2x -24

Solution:

Given, the zeroes of a quadratic polynomial are -3 and 4.

We have to find the quadratic polynomial.

A quadratic polynomial in terms of the zeroes (α,β) is given by

x2 - (sum of the zeroes) x + (product of the zeroes)

i.e, f(x) = x2 -(α +β) x +αβ

Here, α = -3 and β = 4.

Sum of the zeroes = α +β = -3 + 4 = 1

Product of the zeroes = αβ = (-3)(4) = -12

Now, the quadratic polynomial can be written as

x²- (sum of zeroes)x+(product of zeroes)

= x²- (α+ β)x+(αβ)

By substituting the values

= x² - (1)x + (-12)

= x² - x - 12

Dividing the entire equation by 2

= x²/2 – x/2 -12/2

= x²/2 – x/2 -6

Therefore, the quadratic polynomial is x²/2 - x/2 - 6.

✦ Try This: A quadratic polynomial, whose zeroes are -2 and 4, is

Given, the zeroes of a quadratic polynomial are -2 and 4.

We have to find the quadratic polynomial.

A quadratic polynomial in terms of the zeroes (α,β) is given by

x2 - (sum of the zeroes) x + (product of the zeroes)

i.e, f(x) = x2 -(α +β) x +αβ

Here, α = -2 and β = 4.

Sum of the zeroes = α +β = -2 + 4 = 2

Product of the zeroes = αβ = (-2)(4) = -8

Now, the quadratic polynomial can be written as

x²- (sum of zeroes)x+(product of zeroes)

= x²- (α+ β)x+(αβ)

By substituting the values

= x² - (2)x + (-12)

= x² - 2x - 8

Dividing the equation by 2

= x²/2 - x - 4

Therefore, the quadratic polynomial is x²/2 - x - 4

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.1 Problem 2

A quadratic polynomial, whose zeroes are -3 and 4, is a. x2 - x + 12 b. + x + 12 c. x² /2 - x/2 - 6 d. 2 + 2x -24

Summary:

A quadratic polynomial, whose zeroes are -3 and 4, is x² /2 - x/2 - 6.

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