SOLUTION: Does anyone have the answer to these questions? Why do we have to check the solutions when we solve radical equations? The discriminant in the quadratic formula is the expres

Question 550757: Does anyone have the answer to these questions?
Why do we have to check the solutions when we solve radical equations?
The discriminant in the quadratic formula is the expression
If the discriminant in the quadratic formula is a perfect square, then the quadratic equation will have __________________solution

Thank you soooo much!!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
1) Checking solutions allows you to find and eliminate extraneous solutions (solutions of the final equation that were not solutions of the original equation). When you square both sides of a radical equation to find the answer, you risk introducing extraneous solutions. For example as you go from to by squaring both sides, you are adding the extraneous solution . (You can also add extraneous solutions when you multiply both sides of an equation by an expression involving x, or whatever variable you are using).
2) The discriminant in the quadratic formula is the expression , which you see under the square root in the quadratic formula.
3) If the discriminant in the quadratic formula is a perfect square, then the quadratic equation will have rational solution(s). The square root of the discriminant will be a rational number, and so will be the whole expression calculated using the quadratic formula. If the discriminant is zero (which could be called a perfect square), there will be one rational solution. If the discriminant is a positive perfect square, there will be two different rational solutions.
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