Let us consider an example.
Find the solutions for the quadratic equation: 4x2 + 26x + 12 = 0
From the equation, we get a = 4, b = 26 and c = 12. Putting the values into the formula, we get
The following video shows how to use the quadratic formula to find solutions to quadratic equations.
Quadratic equations can have two real solutions, one real solution or no real solution. The number of solutions is determined by the discriminant.
If the discriminant is positive then there are two distinct solutions.
For example, in the quadratic equation 4x2 + 26x + 12 = 0, its discriminant is equals to b2 − 4ac = (26)2 − 4(4)(12) = 484 which is positive and so the equation has two real solutions.
If the discriminant is zero, then there is exactly one real solution.
For example, in the quadratic equation x2 + 4x + 4 = 0, its discriminant is equals to
b2 − 4ac = (4)2 − 4(1)(4) = 0 and so the equation has exactly one real solution.
If the discriminant is negative, then there is no real solution.
For example, in the quadratic equation x2 + x + 5 = 0, its discriminant is equals to
b2 − 4ac = (1)2 − 4(1)(5) = −19 which is negative and so the equation has no real solution.
We then get two values for x.
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