Quadratic Equation Definition:
A quadratic equation is a polynomial equation of the second degree. The general form is
ax^{2}+bx+c=0, where a ≠0.
Quadratic Equation Formula :
ax^{2} + bx + c = 0,
where
a = coefficient of x^{2}
b = coefficient of x and
c = constant.
Quadratic Equation solving formula:
x = ( b ±√ b^{2}  4 * a * c) / 2 * a
Example 1: Calculate the roots(x1, x2) of the quadratic equation,
x^{2} + 2x  8 = 0.
Step 1: From the above equation, the value of a = 1, b = 2 and c =  8.
Step 2: To Find X:
Substitute the values in the formula below
x = ( b ±√ b^{2}  4 * a * c) / 2 * a
Step 3: We get the roots,
x = ( 2 ±√ 2^{2}  4 * 1 *  8) / 2 * 1
x =  4 and x = 2
which means x1 =  4 and x2 = 2.
Example 2: Calculate the roots(x1, x2) of the quadratic equation, x^{2}  10x + 25 = 0
Step 1: From the above equation, the value of a = 1, b =  10 and c = 25.
Step 2: To Find X:
Substitute the values in the formula below
x = ( b ±√ b^{2}  4 * a * c) / 2 * a
Step 3: We get the roots,
x = ( 2 ±√ 2^{2}  4 * 1 *  8) / 2 * 1
x = 5 and x = 5
which means x1 = 5 and x2 = 5.
Here x = 5 is called the double root. A quadratic will have a double root if the quadratic is a perfect
square trinomial.

