Algebra I: Solving with the quadratic formula
This is a free lesson from our course in Algebra I
In this section, you'll learn another approach to using the quadratic formula. If the left hand side of a given equation ax2 + bx + c = 0 cannot be factorized easily into the product of a pair of binomials, then it can be solved by using the quadratic formula x = {-b (b2 - 4ac)}/2a and it'll have two roots. For example, if you use the quadratic formula to solve equation x2 + 2x + 7, you get two roots x = -1 22. There are some quadratics (most of them, actually) that you can't solve by factoring. But the Quadratic Formula will always work, whether the quadratic was factorable or not.(More text below video...)
<h2> Solving with the quadratic formula - Watch video (Algebra I)</h2> <p> solution, quadratic, formula, product, binomials, math help, roots, solved, example, practice questions, quizzes</p> <p> If the quadratic equation cannot be factorized into the product of a pair of binomials, then it can be solved by using the quadratic formula and it&rsquo;ll have two roots.</p>
Other useful lessons:
Solve 2nd order polynomial by factoring
Solution and discriminant in the quadratic formula
Factoring by grouping
(Continued from above) For example, use the Quadratic Formula to solve x2 – 4x – 8 = 0.
Looking at the coefficients, you see that a = 1, b = –4, and c = –8. Plug them into the Formula, and simplify.
x = -(-4) ± (-4)2 – 4(1)(-8) / 2(1)
= 4 ± (16 + 32) / 2
= 4 ± 48 / 2
= 4 ± 43 / 2
= 2 ± 23
= 2(1 ± 3)
Then the solution is x = 2(1 ± 3).
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