Theory question 106
Quadratic Equations(a) Solve the equation, correct to two decimal places. 2x2 + 7x − 11 = 0
(b) Using the substitution p = 1/x, q = 1/y Solve the simultaneous equation 2/x + 1/y = 3, 1/x − 5/y = 7
Show the model answer
Model answer
(a) x = (−7 ± √(49 + 88))/4 = (−7 ± √137)/4 = (−7 ± 11.705)/4
x = 1.18 or x = −4.68
(b) 2p + q = 3 and p − 5q = 7
From the first, q = 3 − 2p; then p − 15 + 10p = 7, so 11p = 22, p = 2 and q = −1
x = 1/p = ½, y = 1/q = −1
Explanation
Solve for p and q first, then turn them back into x and y.