Quadratic Equation Definition:
A quadratic equation is a polynomial equation of the second degree. The general form is
ax2+bx+c=0, where a ≠0.
Quadratic Equation Formula :
ax2 + bx + c = 0,
where
a = coefficient of x2
b = coefficient of x and
c = constant.
Quadratic Equation solving formula:
x = (- b ±√ b2 - 4 * a * c) / 2 * a
Example 1: Calculate the roots(x1, x2) of the quadratic equation,
x2 + 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 ±√ b2 - 4 * a * c) / 2 * a
Step 3: We get the roots,
x = (- 2 ±√ 22 - 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, x2 - 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 ±√ b2 - 4 * a * c) / 2 * a
Step 3: We get the roots,
x = (- 2 ±√ 22 - 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.
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