Theory question 103
Quadratic Equations(a) Given the expression y = ax2 − bx − 12, find the values of x when a = 1, b = 2 and y = 3
(b) If √(x2 + 1) = 5/4 find the positive value of x.
Show the model answer
Model answer
(a) x2 − 2x − 12 = 3, so x2 − 2x − 15 = 0, (x − 5)(x + 3) = 0: x = 5 or x = −3.
(b) x2 + 1 = 25/16, so x2 = 9/16 and the positive value is x = 3/4.
Explanation
Substitute the given values, then rearrange to a quadratic equal to zero.