Question
I. 10x2 + 33x + 9 = 0 II.
2y2 + 13y + 21 = 0 In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.Solution
I. 10x2 + 33x + 9 = 0 => 10x2 + 30x + 3x + 9 = 0 =>10x(x + 3) + 3(x + 3) = 0 => (x + 3) (10x + 3) = 0 => x = -3, -3/10 II. 2y2 + 13y + 21 = 0 =>2y2 + 7y + 6y + 21 = 0 => y(2y + 7) + 3(2y + 7) = 0 => (2y + 7) (y + 3) = 0 => y = -7/2, -3 Hence, x ≥ y. Alternate Method: if signs of quadratic equation is +ve and +ve respectively then the roots of equation will be -ve and -ve. So, roots of first equation = x = -3, -3/10 So, roots of second equation = y = -7/2, -3 After comparing we can conclude that x ≥ y.
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