Theory question 105
Algebraic Expressions(a) Given that (5y − x)/(8y + 3x) = 1/5, find the value of x/y to two decimal places.
(b) If 3 is a root of the quadratic equation x2 + bx − 15 = 0, determine the value of b. Find the other root.
Show the model answer
Model answer
(a) 5(5y − x) = 8y + 3x, so 25y − 5x = 8y + 3x, 17y = 8x and x/y = 17/8 = 2.125 ≈ 2.13.
(b) 32 + 3b − 15 = 0, so 3b = 6 and b = 2.
x2 + 2x − 15 = (x − 3)(x + 5) = 0, so the other root is −5.
Explanation
Cross-multiply, then collect the x and y terms on opposite sides.