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Nature of Roots

Which of the ...

Question

Which of the following equations has two distinct real roots?

2x² - 3 √2 x + 9/4 = 0

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x² + 3x + 2√3 = 0

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5x² - 3x + 1 = 0

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x² + x - 5 = 0

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Solution

The correct option is D
x² + x - 5 = 0

A quadratic equation has two distinct roots if D = b² - 4ac > 0.

Consider the quadratic equation x² + x - 5 = 0.

Here, D = (1)² - 4(1)(-5) = 1 + 20 = 21 > 0

Thus, this equation has two distinct real roots.

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