Solution: Given, the sum of two zeros is -3/2√5. Product of two zeros is -1/2. 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 = -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 factorisationSummary: 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 ☛ Related Questions: |