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

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

0, sqrt5

Solution

0, sqrt5

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

Given α + ß = 0 = –b/a

αß = sqrt5  = c/a

If a = 1, b = 0, c = sqrt5

Therefore, the quadratic polynomial is x2 + sqrt5

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Concept: Relationship Between Zeroes and Coefficients of a Polynomial
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NCERT Class 10 Maths
Chapter 2 Polynomials
Exercise 2.2 | Q 2.3 | Page 33