Find the roots of the following quadratic equations by factoring.
y=x^2+9x-36
I got (x+12)(x-3) but on the answer key it says that the answer is this, however it renames the x values with opposite values.
For example, the answer on the review for it has my answer, but the final answer is x=-12 and x=3. Is this because numbers in the parenthesis are always opposite of what they are? Like a number that is positive will be a negative, and vice-versa?
Thank you.
2 answers
Nevermind got it! it's because it's supposed to equal 0 so you have to solve the equation to make it zero. Basically by doing the inverse of the number but not really.
First of all , let me point out a discrepancy in the wording of your question
The way your equation is written as y = x^2 + 9x - 36
it should have asked for the x-intercepts of the function
To do that , we realize that for an x-intercept, the value of y = 0
so your function becomes the quadratic equation
x^2 + 9x - 36 = 0 , which factors to
(x+12)(x-3) = 0 , .............. you had that.
Please agree with my following argument:
If two numbers are multiplied and the answer is zero, then one of the multipliers, or both, must have been zero.
But we don't know which one, so we say:
x+12 = 0 -----> x = -12
or
x-3 = 0 -----> x = 3
What you did was FACTOR the expression, but it asked for the roots.
Can you see why the signs would always change?
(Because we are taking the constant to the other side of the equal sign)
e.g. if one of factors had been 3x + 5
we would say:
3x+5 = 0
3x = -5
x = -5/3
The way your equation is written as y = x^2 + 9x - 36
it should have asked for the x-intercepts of the function
To do that , we realize that for an x-intercept, the value of y = 0
so your function becomes the quadratic equation
x^2 + 9x - 36 = 0 , which factors to
(x+12)(x-3) = 0 , .............. you had that.
Please agree with my following argument:
If two numbers are multiplied and the answer is zero, then one of the multipliers, or both, must have been zero.
But we don't know which one, so we say:
x+12 = 0 -----> x = -12
or
x-3 = 0 -----> x = 3
What you did was FACTOR the expression, but it asked for the roots.
Can you see why the signs would always change?
(Because we are taking the constant to the other side of the equal sign)
e.g. if one of factors had been 3x + 5
we would say:
3x+5 = 0
3x = -5
x = -5/3