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Question
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
Options
two distinct real roots
two equal real roots
no real roots
more than two real roots
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Solution
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has no real roots.
Explanation:
Given equation is `2x^2 - sqrt(5)x + 1` = 0
On comapring with ax2 + bx + c = 0, we get
a = 2, b = `-sqrt(5)` and c = 1
∴ Discriminant, D = b2 – 4ac
= `(-sqrt(5))^2 - 4 xx (2) xx (1)`
= 5 – 8
= – 3 < 0
Since, discrimant is negative,
Therefore quadratic equation `2x^2 - sqrt(5)x + 1` = 0 has no real roots
i.e., imaginary roots.
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