Question

x^2-2x+5 = 0
help me
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Answer 1

Answer:

No real roots exists.

Step-by-step explanation:

We may find the roots of thw given equation by quadratic method. As we don't get perfect factors when seen through factorisation method.

By using quadratic formula,

x = $\large{\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}$

We know,

a = 1 ; b = - 2 ; c = 5

Putting up the values,

x = $\frac{-(-2) \pm \sqrt{(-2)^2 - 4 \times 1 \times 5}}{2 \times 1}$

x = $\frac{2 \pm \sqrt{4 - 20}}{2}$

x = $\frac{2 \pm \sqrt{-16}}{2}$

But we know that, number inside the roots cannot be negative.

So no real roots exists.

You may also try completing the square method.

You know, many of us are worried about the nature of the roots when they have to find the roots of any given equation.

You may also find out the nature of the roots by finding out discriminate value.

Discriminate (d) = b^2 - 4ac

If b^2 - 4ac > 0, then the roots are real and distinct.

If b^2 - 4ac = 0, then the roots are real and equal.

If b^2 - 4ac < 0, then the roots doesn't exist.