Question

Given that x=1.5 is the only solution to the equation 4x^2 - ax + b = 0, find the values of a and b. Show all workings.

Answer: a = 12, b = 9

Answer 1

If x = 1.5 is the only solution to the equation 4x² - ax + b =0 then

4x² - ax + b = 4(x - 1.5)²      |use p² - 2pq + q² = (p - q)²

4x² - ax + b = 4(x² - 2x · 1.5 + 1.5²)

4x² - ax + b = 4(x² - 3x + 2.25)

4x² - ax + b = 4x² - 12x + 9  |subtract 4x² from both sides

-ax + b = -12x + 9

therefore

-a = -12 ⇒ a = 12 and b = 9