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Question
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 1)(x – 2) + x = 0
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Solution
The equation (x + 1)(x – 2) + x = 0 has two real and distinct roots.
Simplifying the above equation,
x2 + x – 2x – 2 + x = 0
x2 – 2 = 0
D = b2 – 4ac
= (0)2 – 4(1)(–2)
= 0 + 8 > 0
Hence, the roots are real and distinct.
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