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Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively. 0,5 - Mathematics

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Question

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

`0, sqrt5`

Sum
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Solution

Given: α + β = 0, αβ = `sqrt5`

Since ax2 + bx + c = k[x2 - (α + β)x + αβ]

Or `(ax^2 + bx + c)/k = (x^2 - 0x + sqrt5)`

or `(ax^2 + bx + c)/k = (x^2 + sqrt5)/1`

Here k is a constant term, by comparing k = 1

Hence, ax2 + bx + c = `x^2 + sqrt5`

The quadratic polynomial is `x^2 + sqrt5`.

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Chapter 2: Polynomials - Exercise 2.2 [Page 33]

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NCERT Mathematics [English] Class 10
Chapter 2 Polynomials
Exercise 2.2 | Q 2.3 | Page 33

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