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Nature of Roots

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Question

Check whether the following equation will have two distinct real or imaginary or two real equal roots.
$x^{2} - 3 x + 5 = 0$ .

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Solution

Given the quadratic equation is
$x^{2} - 3 x + 5 = 0$ .

Now discriminant of this equation will be
$b^{2} - 4 a c = (- 3)^{2} - 4 \times 5 \times 1$
$= 9 - 20$
$= - 11$ .

As the discriminant $< 0$ then the quadratic equation will have imaginary roots.

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has real roots or no.

Check whether the roots of the following quadratic equations are real or not?

3 x^{2} - 4 \sqrt{3} x + 4 = 0

.

The nature of roots of $x^{2} - 3 x + 2 = 0$ will be:

The equation $x^{2} + x - 5 = 0$ has two distinct real roots.

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