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Question
Which of the following equations has two distinct real roots?
Options
`2x^2 - 3sqrt(2)x + 9/4 = 0`
`x^2 + x - 5 = 0`
`x^2 + 3x + 2sqrt(2) = 0`
`5x^2 - 3 + 1 = 0`
Solution
x2 + x – 5 = 0
Explanation:
The given equation is x2 + x – 5 = 0
On comparing with ax2 + bx + c = 0, we get
a = 1, b = 1 and c = – 5
The discriminant of x2 + x – 5 = 0 is
D = b2 – 4ac
= (1)2 – 4(1)(–5)
= 1 + 20
= 21
⇒ b2 – 4ac > 0
So, x2 + x – 5 = 0 has two distinct real roots.
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