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Roots Calculator
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A Root is a value of any given function which when substituted in that function gives the answer as zero. Roots Calculator for a polynomial calculates the root of any given polynomial function.

## Steps for Roots Calculator

Step 1 :

Observe the given quadratic equation of the form ax2 + bx + c and write down the values of a,b,c. Then find the discriminant D using the formula:
D = b2 - 4ac

Step 2 :

Based on the value of discriminant the roots changes
If the value of discriminant is less than zero then roots are imaginary or does not exist.
If the value of discriminant is greater then or equal to zero then we can find root of the equation using the formula:
x = $\frac{-b \pm \sqrt{D}}{2a}$
where x1 = $\frac{-b + \sqrt{D}}{2a}$ and

x2 = $\frac{-b - \sqrt{D}}{2a}$ are the two roots.

## Problems on Roots Calculator

1. ### Solve: x2 + 5x + 6 = 0

Step 1 :

Given equation is: x2 + 5x + 6 = 0

where a = 1, b = 5, c = 6

The Discriminant is calculated using the formula:

D = b2 - 4ac

= 25 - 4(1)(6)

= 25 - 24

= 1.

Step 2 :

Since the value of D is positive, use the formula:

x1$\frac{-b + \sqrt{D}}{2a}$

= $\frac{-5 + \sqrt{1}}{2 \times 1}$

= -2

x2$\frac{-b - \sqrt{D}}{2a}$

= $\frac{-5 - \sqrt{1}}{1}$

= -3.

The roots for x2 + 5x + 6 are x1 = -2 and x2 = -3.

2. ### Solve: 2x2 - 2x + 4 = 0

Step 1 :

Given equation is 2x2 - 2x + 4

where a = 2, b = -2, c = 4

The discriminant is given by

D = b2 - 4ac

= (-2)2 - 4 (2)(4)

= -28.

Step 2 :

Since the discriminant is negative, the roots are imaginary.

x1$\frac{-b + \sqrt{D}}{2a}$

= $\frac{2 + \sqrt{-28}}{2 \times 2}$

= 0.5 + i(1.3228)

x2$\frac{-b - \sqrt{D}}{2a}$

= $\frac{2 - \sqrt{-28}}{2 \times 2}$

= 0.5 - i(1.3228)