Question 258512: Compute the discriminate. Determine the number and the type of solutions for the given equation
10x^2=20x-10
Answer by Nikki456(9)   (Show Source):
You can put this solution on YOUR website! Okay. So discriminant has a formula. The formula is  . In discriminant, there are different types of solutions to equations. The types solutions are:
1) When D>0, then there are two different real number solutions.
2) When D=0, then there is a repeated solution.
3) When D<0, then there are two different complex number solutions.
I'm assuming that you know about real and complex numbers since you're doing this level of math. Now, you may notice that in discriminant, the formula is very similar to the quadratic equations formula (in case you don't know then the formula is x= -b +- sqrt.(b^2-4*a*c)/(2*a) . Now, getting back to your problem.
Okay, so your problem is 10x^2=20x-10. To make the equation simpler, you could divide the whole thing by 10. So you would get x^2=10x-1. So this is a lot simpler. You subtract x^2 on both sides leaving you with -x^2+10x-1=0. You could multiply the whole equation by -1 to get rid of the negative on the x^2. Now you get x^2-10x+1=0. Now you suppose 1 is a (because in front of the x^2 in the equation is actually a 1), 10 is b, and 1 is c. Now all you have to do is plug these values into the discriminant formula, .
So D= (-10)^2 -4(1)(1). You get 100-4. This leaves you with D= 96>0. So this has two different real number solutions.
So your answer:
D=96>0
You have two different real number solutions.
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