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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
Solution
(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
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