Question
I. 12y2Β + 11y β 15 = 0 II.
8x2Β β 6x β 5 = 0Solution
I. 12y2 + 11y β 15 = 0 12y2 β 9 y + 20y β 15 = 0 3 y(4 y β 3) + 5(4 y β 3) = 0 (3 y + 5) (4 y β 3) = 0 y = 3/4, -5/3 II. 8x2 β 6x β 5 = 0 8x2 β 10x + 4x β 5 = 0 2x(4x β 5) + 1(4x β 5) = 0 (4xΒ β 5) (2 x+1) = 0 x = 5/4, -1/2 Hence, relationship cannot be established between x and y. Alternate Method: Remember whenever roots of x & y are + & - both, there is no need to find the exact value of roots. In this case, there will be always no relation between x & y. Hence relationship between x & y cannot be established.
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