Find quadratic equation using the Quadratic Formula:
Solve the subsequent quadratic equation using the Quadratic Formula.
4x^{2} + 2 = x^{2} - 7x:
Solution:
Step 1. Write the equation in general forms.
4x^{2} + 2 = x^{2} -7x
3x^{2} + 7x + 2 = 0
a= +3, b = +7, c = +2
Step 2.
x = (6 ± √20)/2
x = 3 ± 1/2√20
x = 3 ± √5
x = 3 + √5, 3 - √5
x = 3 + 2.236, 3 -2.236
x = 5.236, 0.746
Step 3. Check the roots.
2x^{2} + 4 = 6x +x^{2}
2(3 + √5)^{2} +4 = 6(3 + √5) + (3+√5)^{2}
2(9 + 6√5 + 5) + 4 = 18 +6√5 + 9 + 6√5 + 5
18 + 12√5 + 10 + 4 = 18 + 12√5 + 9 +5
32+ 12√5 = 32 + 12√5
And,
2x^{2} + 4 = 6x + x^{2}
2(3-√5)2 + 4 = 6(3- √5) + (3 - √5)2
2(9-6√5 + 5) + 4 = 18-6√5 + 9 -6√5 + 5
18 - 12√5 + 10 + 4 = 18 - 12√5 + 9 + 5
32- 12√5 = 32 - 12√5
Thus, the roots check.
The Quadratic Formula can be used to search the roots of any quadratic equation. For a pure quadratic equation in that the numerical coefficient b equals zero, the Quadratic Formula (2-8) decreased to the formula given as Equation 9.
For b = 0, this decreases to the subsequent.