Question

Using quadratic formula, find the roots of the following equations: x^2_2x+5=0​

Answer 1

No roots exist.

Step-by-step explanation:

Correct Question:

Using quadratic formula, find the roots of the following equations: x²-2x+5.

Solution:

First, let us note down the values of a, b and c in the given quadratic equation:

• a = 1
• b = -2
• c = 5

Quadratic formula is a method to find the roots of a quadraic equation. According to this method:

$\longrightarrow{x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}}$

Before applying the values, we need to find the discriminant of the given equation. Discriminant tells us whether roots are real or not real. If the roots are real, we can further proceed with quadratic formula. If not, roots does not exists.

In a quadratic equation ax²+bx+c,

• b²-4ac > 0  (Roots are real and distinct)
• b²-4ac = 0  (Roots are real and equal)
• b²-4ac < 0  (Roots are unreal)

→ Discriminant = b²-4ac

→ Discriminant = (-2)²-4×1×5

→ Discriminant = 4-20

→ Discriminant = -16

Since, -16 < 0, we can say that the roots does not exist.

No root exists!

Answer 2

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