Question

Given that the sum of the zeroes of the polynomial (a +1)x2+(2a +3)x+ (3a + 4) is -1. Find the product of its zeroes.

JEE/Engineering Exams

Maths

Solution

115

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since the sum of the zeroes of the quadratic polynomial ( (a+1) x^{2}+(2 a+3) x+(3 a+4) ) is -1 ( therefore frac{-(2 a+3)}{a+1}=-1 ) [ left[because text { Sum of zeroes }=frac{-(text { Coefficient of } mathbf{x})}{text { coefficient of } mathbf{x}^{2}}right] ] ( Rightarrow a+1=2 a+3 Rightarrow a=-2 ) Now, product of zeroes ( =frac{3 a+4}{a+1}=frac{3(-2)+4}{-2+1}=2 ) ( left[because text { Product of zeroes }=frac{text { Constant term }}{text { Coefficient of } mathbf{x}^{2}}right] )