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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively 4, 1 - Mathematics

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

4, 1

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Solution

4,1

Let the quadratic polynomial be ax2 + bx + c, and its zeroes be α and ß

Given α + ß = 4 = `–b/a`

αß = 1 = `c/a`

If a = 1, then b = -4, c = 1

Therefore, the quadratic polynomial is x2 – 4x +1.

Concept: Relationship Between Zeroes and Coefficients of a Polynomial
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APPEARS IN

NCERT Class 10 Maths
Chapter 2 Polynomials
Exercise 2.2 | Q 2.6 | Page 33
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