I need to find x of the quadratic function y=-3/4x^2-4x-1 and keep getting (4)/(3/2). Is this right and if so, can it be reduced?
I assume you want to find the roots of the polynomial (saying "find x" is meaningless).
Just use the quadratic formula:
x = [4 ±√(16-4(-3/4)(-1))]/[2(-3/4)]
= (-8±2√13)/3
To find the x-values of the quadratic function y = (-3/4)x^2 - 4x - 1, we can set y equal to zero and solve for x.
0 = (-3/4)x^2 - 4x - 1
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = (-3/4), b = -4, and c = -1.
Plugging in these values, we get:
x = (4 ± √((-4)^2 - 4(-3/4)(-1))) / (2(-3/4))
Simplifying:
x = (4 ± √(16 - 3)) / (-3/2)
x = (4 ± √13) / (-3/2)
To simplify further, we can multiply the numerator and denominator by 2 to eliminate the fraction in the denominator:
x = ((4 ± √13) / 1) / (-3/2)
x = (4 ± 2√13) / (-3)
So, the solutions for x are:
x = (4 + 2√13) / (-3) and x = (4 - 2√13) / (-3)
Therefore, the answer you obtained, (4)/(3/2), is not correct. The correct solutions can be expressed in the form:
x = (4 ± 2√13) / (-3)