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What can be said about the quadratic equation $x 2 − 5 x + 3 = 0 ?$

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The given quadratic equation

x 2 − 5 x + 3 = 0

has real and distinct roots.

The given quadratic equation

x 2 − 5 x + 3 = 0

has complex roots.

The given quadratic equation

x 2 − 5 x + 3 = 0

has equal real roots.

None

answer is A.

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Detailed Solution

The given equation is

x 2 − 5 x + 3 = 0.

An equation in the form

a x 2 + b x + c = 0, a ≠ 0

is called quadratic equation in one variable x, where a, b, c are constants.
We use discriminant (D) to determine if a given equation is real or not.

D = b 2 − 4 a c

D > 0

then equation therefore has two different and real roots.
If

D = 0

then equation has equal and real roots.
If

D < 0

then equation has no real roots.
The discriminant of the given quadratic equation

x 2 − 5 x + 3 = 0.

Discriminant = (− 5) 2 − 4 × 3 × 1 = 25 − 12 = 13

As we can observe, the discriminant of the given equation is positive.
Hence, the given quadratic equation

x 2 − 5 x + 3 = 0

has real and distinct roots.
The correct option is (1).

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What can be said about the quadratic equation $x 2 − 5 x + 3 = 0 ?$