Question 115339: the directions on this work sheet is use the quadratic formula to solve each equation and the equation is m^2+5m-6=0 i dont understand how to figure it out so if you could give me directions so that i know how to get the answer i would be greatly appriciated! thanks
Answer by aka042(26)   (Show Source):
You can put this solution on YOUR website! This is in response to a follow up from the student to clarify. My original solution remains below:
m actually equals two numbers, 1 and - 6.
The quadratic equation deals with the coefficients of the equation you are trying to solve. Your equation is some coefficient a * m^2 + some coefficient b * m - 6, which we will call c. Remember that a coefficient is the number that falls before your x term. We have two x terms, x^2 and x, so two coefficients, a and b.
In general form, the quadratic equation states that m = ( b + or - the square root of (b^2 - 4ac)) all divided by 2*a.
So the quadratic equation first tells you to first solve for b^2 - 4 * a * c. For your specific equation: b, the number that appears before "m", is 5. a, the number that appears before m^2, is 1. And finally c, is -6. Therefore b^2 = 5^2 = 25, and 4 * a * c = 4 * 1 * -6 = -24. So b^2 - 4*a*c = 25 - (-24) = 25 + 24 = 49.
Next, we need to take the square root of that. The square root of 49 is 7.
After this, we need to split into two different equations: -b + 7 and -b - 7. Knowing that b is 5, -b must be -5, so we have -5 + 7 =2 and -5 - 7 = -12.
Finally, we need to divide both equations by 2 * a, or 2*1 = 2. 2/2 = 1, so your first solution is 1. -12/2 = -6, so your second solution is -6. Your answer is m = 1 and m = -6.
Let's plug in to make sure: 1(1)^2 + 5(1) - 6 = 1 + 5 - 6 = 6- 6 = 0. This fits your original equation so 1 is definitely a solution.
1(-6)^2 + 5(-6) - 6 = 36 - 30 - 6 = 6 - 6 = 0, so -6 is also definitely a solution.
Therefore your answers are m = 1 and m = -6.
It may be a little confusing that an equation yields two solutions. However, what you are doing is solving for when the given parabola crosses the line x= 0. Since a parabola is symmetrical, this happens two times, yielding two solutions.
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Quadratic equations are typically expressed in terms of x, however the variable you use does not matter (in this case m).
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Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=49 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 1, -6.
Here's your graph:
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