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-3/2√5, -½ find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation

Solution:

Given, the sum of two zeros is -3/2√5.

We have to find the quadratic polynomial and its zeros.

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, sum of the roots, α +β = -3/2√5

Product of the roots, αβ = -1/2

So, the quadratic polynomial can be written as x² - (-3/2√5)x + (-1/2)

= x² + 3/2√5x - 1/2.

= 2√5x² + 3x - √5

Let 2√5x² + 3x - √5 = 0

On factoring the polynomial,

2√5x² - 2x + 5x - √5 = 0

2x(√5x - 1) + √5(√5x - 1) = 0

(2x + √5)(√5x - 1) = 0

Now, 2x + √5 = 0

2x = -√5

x = -√5/2

Also, √5x - 1 = 0

√5x = 1

x = 1/√5

Therefore, the zeros of the polynomial are 1/√5 and -√5/2

✦ Try This: Find a quadratic polynomial, the sum and product of whose zeroes are -√5 and 5√5, respectively. Also find its zeroes

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

NCERT Exemplar Class 10 Maths Exercise 2.4 Problem 1 (iv)

-3/2√5 and -½ find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation

Summary:

A quadratic polynomial whose sum and product of zeroes are -3/2√5 and -1/2 is 2√5x² + 3x - √5. The zeros of the polynomial are 1/√5 and -√5/2

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