Determine if the given value is a solution for each quadratic. Answer yes or no.
2x^2-3x(root 2)+2=0
I know the answer is yes but I don't know how to get to that answer.
Thanks a ton! :)
Kayla
roots:
x=(3*sqrt2+-sqrt(18-16))/4
so those are the values.
Just to simplify a bit,
(3√2±√2)/4 = √2 or √2/2
So to find that I would need to go into decimals & leave exact form & then square my final answer to know that my answer was the root of 2?
To determine if a given value is a solution for a quadratic equation, you can substitute the value into the equation and check if it satisfies the equation. In this case, you have the equation 2x^2 - 3x√2 + 2 = 0 and you want to check if a given value is a solution.
Let's say the given value is x = a.
To check if x = a is a solution, substitute a in place of x in the equation and simplify:
2(a)^2 - 3(a)√2 + 2 = 0
This simplifies to:
2a^2 - 3a√2 + 2 = 0
Now, you need to solve this equation. It is in the form of a quadratic equation, so you can use the quadratic formula to find the solutions. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the equation we have with the quadratic formula, we can identify the values of a, b, and c:
a = 2
b = -3√2
c = 2
Now, substitute these values into the quadratic formula:
x = (3√2 ± √((-3√2)^2 - 4(2)(2))) / (2(2))
Simplifying further:
x = (3√2 ± √(18 - 16)) / 4
x = (3√2 ± √2) / 4
As you can see, we have two possible solutions:
x = (3√2 + √2) / 4 --> One solution
x = (3√2 - √2) / 4 --> Another solution
Since we have two solutions, any of these values of x would be a solution to the quadratic equation. Therefore, if the given value is equal to any of these solutions, the answer is yes. In this case, since we don't have a specific value for a, we cannot definitively say if it is a solution.