Solve the quadratic equation.
3x^2-15x+18=0
I know that the formula to quadratic equation is x=-b+and-(square root)b^2-4ac divided by 2a.
I know that a=3, b=-15 and c=18, then subsitute in and get two answers, my problem is that I keep getting an answer that does not work after I subsitute in the original equation. What do I do?
did you get
x = (15 ± √(225 - 4(3)(18) )/6 ?
= (15 ± √9)/6
= (15 ±3)/6
= 3 or 2
we could have divided the original equation by 3 to get
x^2 - 5x + 6 = 0
now it factors
(x-3)(x-2) = 0
so x = 3 or x = 2
I got 3 and -2. But to check it, wouldn't you substitue it the 3 and then the -2 in the original equation and it should be 0=0?
and so it does
How did you get -2?
if you had a + and a - then you couldn't possible end up with +18 at the end.
if x= 3
3(9) - 45 + 18 = ??
if x=2
3(42) - 30 + 18 = ???
If you have correctly substituted the values of a, b, and c into the quadratic formula and are still getting an answer that does not work when you substitute back into the original equation, there are a few possible explanations:
1. Calculation error: Double-check your calculations to make sure you haven't made any mistakes when substituting the values into the formula or when simplifying the equation.
2. No real solutions: It is possible that the quadratic equation does not have any real solutions. This occurs when the discriminate, b^2 - 4ac, is negative. In this case, you would not be able to find any real values for x that satisfy the equation. Instead, you would end up with two complex conjugate solutions.
To determine whether the quadratic equation has real solutions or not, calculate the discriminate (b^2 - 4ac) and check if it is positive, negative, or zero.
In the given equation, a = 3, b = -15, and c = 18. Plugging these values into the discriminate:
b^2 - 4ac = (-15)^2 - 4(3)(18) = 225 - 216 = 9
Since the discriminate is positive (9 > 0), the quadratic equation does have real solutions.
Therefore, it seems that there may have been an error in your calculations. Double-check your steps and try solving the equation again.