let f(x) = 12x^2 +7x-10. Find x such that f(x)=0
a.) -4/5, 5/3
b.) -5/4, 2/3
c.) -2/5, 5/3
d.) -5/3, 2/3
solve 12x^2 + 7x - 10 = 0
Hint: it factors
If you can't see or find the factors use the quadratic formula
I think I have it I was able to factor out 12x^2 +7x-10 to (4x+5) (3x-2)=0
answer is -5/4 and 2/3
right?
To find the values of x such that f(x) = 0, we need to solve the quadratic equation 12x^2 + 7x - 10 = 0.
There are different methods to solve quadratic equations, but one common method is factoring. However, in this case, the given quadratic equation does not easily factor. Therefore, we'll use the quadratic formula.
The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For our equation 12x^2 + 7x - 10 = 0, we have a = 12, b = 7, and c = -10. Plugging these values into the quadratic formula, we get:
x = (-7 ± sqrt(7^2 - 4 * 12 * -10)) / (2 * 12)
= (-7 ± sqrt(49 + 480)) / 24
= (-7 ± sqrt(529)) / 24
= (-7 ± 23) / 24
This gives us two possible values for x:
1. When x = (-7 + 23) / 24 = 16 / 24 = 2 / 3
2. When x = (-7 - 23) / 24 = -30 / 24 = -5 / 4
Therefore, the correct answer is b.) -5/4, 2/3.