I. 2x2 + 13x + 21 = 0 II.

Solution

I. 2x² + 13x + 21 = 0 => 2x² + 6x + 7x + 21 = 0 => 2x(x + 3) + 7(x + 3) = 0 => (x + 3) (2x + 7) = 0 => x = -3, -7/2 II. 3y² + 34y + 63 = 0 => 3y² + 27y + 7y + 63 = 0 => 3y(y + 9) + 7(y + 9) = 0 => (y + 9) (3y + 7) = 0 => y = -9, -7/3 Hence, relation cannot be established between x and 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, -7/2 So, roots of second equation = y = -9, -7/3 After comparing we can conclude that relationship cannot be established between x and y.