Question

Write the following equation in the form ax² + bx + c = 0, then write the values of a, b, c for the equation.

 (x – 1)² = 2x + 3

Answer 1

(x – 1)² = 2x + 3  

(a − b)² = a² − 2ab + b²

∴ x² − 2 × x × 1 + 1² = 2x + 3

∴ x² − 2x + 1 = 2x + 3

∴ x² − 2x − 2x + 1 − 3 = 0

∴ 1x² − 4x − 2 = 0

∴ 1x² + (−4)x + (−2) = 0

Comparing the above equation with ax² + bx + c = 0, we get

a = 1, b = −4, c = −2