State whether the equation (x+1)(x-2)+x=0 has two distinct real roots or not . Justify your answer
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(x+1)(x-2)+x=0 has two distinct real roots
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Answer:
Given, (x + 1) (x – 2) + x = 0
Simplifying above equation we have:
⟹ x2 + x – 2x – 2 + x = 0
=> x2 - 2x + x + x + 2 = 0
⟹ x2 – 2 = 0
⟹ x2 + 0 x – 2 = 0
On comparing with ax2 + bx + c = 0, we have
a = 1, b = 0 and c = –2
Now, D = b2 –4ac = (0)2 – 4(1) (–2) = 0 + 8 = 8 > 0
Hence, the equation (x + 1) (x – 2) + x = 0 has two distinct real roots.
Step-by-step explanation:
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