Determine the zeros of the function 3x^2 -8=10x. I know I rewrite it as 3x^2 -10x-8 = 0
But then what do I do-I'm totally confused-Answers are
{-2,4}
{2,4}
{-2/3,4}
{2/3,4}
Please direct me or show the steps, just don't give me the answer because I still won't get it.
Thank you
What factors does 8 have (8,1 or 4,2?) that, when one is multiplied by 3, will add/subtract to get -10?
4*3 = 12, when you subtract 2 from that product, that give you 10. Just make sure you get the signs right.
(3x+2)(x-4) = 0
To find the zeros of the quadratic equation 3x^2 - 10x - 8 = 0, you can use the quadratic formula or factorization method. Let's go through both methods step by step:
Method 1: Quadratic Formula
The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / 2a, where ax^2 + bx + c = 0.
In our case, a = 3, b = -10, and c = -8. Substituting these values into the quadratic formula, we have:
x = (-(-10) ± √((-10)^2 - 4 * 3 * (-8))) / (2 * 3)
= (10 ± √(100 + 96)) / 6
= (10 ± √196) / 6
= (10 ± 14) / 6
Simplifying further, we get two possible solutions:
1. x = (10 + 14) / 6 = 24 / 6 = 4
2. x = (10 - 14) / 6 = -4 / 6 = -2/3
Hence, the zeros of the function are x = -2/3 and x = 4.
Method 2: Factoring
To factorize the quadratic equation 3x^2 - 10x - 8 = 0, we need to find two numbers whose product is ac (in this case, -24) and whose sum is b (in this case, -10).
We can write the equation as 3x^2 - 12x + 2x - 8 = 0, which can be rearranged as 3x(x - 4) + 2(x - 4) = 0.
Factoring out the common factor (x - 4), we have:
(x - 4)(3x + 2) = 0
Setting each factor equal to zero gives us two possible solutions:
1. x - 4 = 0, which gives x = 4
2. 3x + 2 = 0, which gives 3x = -2, and x = -2/3
Again, we obtain the same zeros of the function: x = -2/3 and x = 4.
So, the correct answer is {-2/3, 4}, which matches option {2/3, 4} you provided.