Theory question 103
Quadratic Equations(a) The value of the expression 2Ax − Kx2 is 7 when x = 1 and 4 when x = 2. Find the values of the constants A and K.
(b) Solve the equation x2 − 3x − 1 = 0, giving your answers correct to 1 decimal place.
Show the model answer
Model answer
(a) x = 1: 2A − K = 7. x = 2: 4A − 4K = 4, i.e. A − K = 1.
Subtract: A = 6, then K = 5.
(b) x = [3 ± √(9 + 4)]/2 = (3 ± √13)/2 = (3 ± 3.606)/2.
x ≈ 3.3 or x ≈ −0.3.
Explanation
Substitute each given x value to get two simultaneous equations.