I. 5x² - 24 x + 28 = 0
II. 4y² - 8 y - 12= 0
I. 5x² - 24 x + 28 = 0 5x² - 14x - 10x + 28 = 0 x (5x – 14) – 2 (5x – 14 ) (x – 2 ) (5x – 14) x = 14/5, 2 II. 4y² - 8y - 12 = 0 4y²- 12y + 4y - 12 = 0 4 (y – 3) + 4(y – 3 ) (y– 3) (4y + 4) y = 3, -1 Hence, relationship between x and y cannot be established. 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 = 14/5, 2 If signs of quadratic equation is -ve and -ve respectively then the roots of equation will be +ve and -ve. (note: -ve sign will come in smaller root) So, roots of second equation = y = 3, -1 After comparing roots of quadratice eqution we can conclude that relation cannot be established between x and y.
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