Question
I. 12y2 + 11y – 15 = 0 II.
8x2 – 6x – 5 = 0Solution
I. 12y2 + 11y – 15 = 0 12y2 – 9 y + 20y – 15 = 0 3 y(4 y – 3) + 5(4 y – 3) = 0 (3 y + 5) (4 y – 3) = 0 y = 3/4, -5/3 II. 8x2 – 6x – 5 = 0 8x2 – 10x + 4x – 5 = 0 2x(4x – 5) + 1(4x – 5) = 0 (4x – 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.
I. y² - 7 y – 18 = 0
II. x² + 10 x + 16 = 0
I. 2x² - 11x + 12 = 0
II. 12y² + 29y + 15 = 0
I. 40x² + 81x + 35 = 0
II. 63y² + 103y + 42 = 0
I. 3p² - 11p + 10 = 0
II. 2q² + 13q + 21 = 0
I. 2x2 – 19x + 45 = 0
II. y2 – 14y + 48 = 0
If the roots of the quadratic equation 6m² + 7m + 8 = 0 are α and β, then what is the value of [(1/α) + (1/β)]?
 If x satisfies x² – 14x + 40 = 0, find x.
I. 81x - 117√x + 40 = 0
II. 81y - 225√y + 136 = 0
If the roots of the quadratic equation 5x² + 4x + 6 = 0 are α and β, then what is the value of [(1/α) + (1/β)]?
...I. 4x² - 21 x + 20 = 0
II. 8y² - 22 y + 15 = 0
