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Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2, respectively. Also find its zeroes

Solution:

Given, the sum of two zeros are 2.

Product of two zeros is -3/2.

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 = √2

Product of the roots, αβ = 3/2

So, the quadratic polynomial can be written as x² - √2x - 3/2.

The polynomial can be rewritten as (1/2)[2x² - 2√2x - 3].
Let 2x² - 2√2x - 3 = 0

On factoring the polynomial,

2x² + √2x - 3√2x - 3 = 0

√2x(√2x + 1) - 3(√2x + 1) = 0

(√2x - 3)(√2x + 1) = 0

Now, √2x - 3 = 0

√2x = 3

x = 3/√2

Also, √2x + 1 = 0

√2x = -1

x = -1/√2

Therefore, the zeros of the polynomial are -1/√2 and 3/√2

✦ Try This: Find a quadratic polynomial, the sum and product of whose zeroes are 2 and 3/2, respectively. Also find its zeroes

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

NCERT Exemplar Class 10 Maths Exercise 2.4 Solved Problem 1

Summary:

A quadratic polynomial whose sum and product of zeroes are √2 and 3/2 is x² - √2x + 3/2= 0. The zeros of the polynomial are -1/√2 and 3/√2

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