Theory question 112
Quadratic Equations(a) Using completing the square method, solve, correct to 2 decimal places, the equation 3y2 − 5y + 2 = 0.
(b) Given that M = (1 2 / 4 3), N = (m x / n y) and MN = (2 1 / 3 4), find the matrix N.
Show the model answer
Model answer
(a) y² − (5/3)y = −⅔ → (y − 5/6)² = 25/36 − 24/36 = 1/36
y − 5/6 = ±1/6 → y = 1.00 or y = 0.67
(b) MN = (m + 2n x + 2y / 4m + 3n 4x + 3y) = (2 1 / 3 4)
m + 2n = 2 and 4m + 3n = 3 → n = 1, m = 0
x + 2y = 1 and 4x + 3y = 4 → y = 0, x = 1
N = (0 1 / 1 0)
Explanation
Matrices are written row by row: (a b / c d) means top row a b, bottom row c d.