Use quadratic formula to solve:
5x^2-10x+6=0
so, what don't you know abouth the formula? You have
a = 5
b = -10
c = 6
Now just plug them into the formula.
I got the answer 10 plus or minus square root of -2 equals 0....not sure if that's the final answer or not
You can always use wolframalpha.com to verify your work. For example,
http://www.wolframalpha.com/input/?i=5x^2-10x%2B6%3D0
You got 10±√-2
That is clearly wrong. The formula states
x = [-b±√(b^2-4ac)]/2a
= [10±√(100-120)]/10
= (10±√-20)/10
= (10±2√-5)/10
= 1±√-5/5
= 1 ± 1/√5 i
I expect that you can now find your mistake(s)
At the very least you cannot say 10±√-2 = 0
To solve the quadratic equation 5x^2 - 10x + 6 = 0 using the quadratic formula, follow these steps:
Step 1: Identify the coefficients a, b, and c in the equation ax^2 + bx + c = 0. In this case, we have a = 5, b = -10, and c = 6.
Step 2: Substitute the values of a, b, and c into the quadratic formula, which is given by x = (-b ± √(b^2 - 4ac)) / (2a).
Step 3: Calculate the discriminant, which is the expression inside the square root (√(b^2 - 4ac)). The value of the discriminant helps determine the nature of the solutions. In this case, the discriminant is b^2 - 4ac = (-10)^2 - 4(5)(6) = 100 - 120 = -20.
Step 4: Since the discriminant (-20) is negative, it implies that the quadratic equation has no real solutions. Instead, we will have complex solutions that involve imaginary numbers.
Step 5: Substitute the values of a, b, and c, along with the discriminant, into the quadratic formula and calculate both roots:
x = (-(-10) ± √(-20)) / (2 * 5)
= (10 ± √(-20)) / 10
At this point, the square root of a negative number (√(-20)) presents an obstacle since we need to simplify it. We can express the square root of -20 as the square root of 20 multiplied by the square root of -1, which is denoted by i:
x = (10 ± √(4 * 5) * i) / 10
= (10 ± 2√5i) / 10.
Now, simplifying further:
x = (10 + 2√5i) / 10 = 1 + √5i
x = (10 - 2√5i) / 10 = 1 - √5i
Therefore, the solutions to the given quadratic equation are x = 1 + √5i and x = 1 - √5i. These are complex solutions involving the imaginary unit i.