document.write( "Question 550757: Does anyone have the answer to these questions?\r
\n" ); document.write( "\n" ); document.write( "Why do we have to check the solutions when we solve radical equations?\r
\n" ); document.write( "\n" ); document.write( "The discriminant in the quadratic formula is the expression\r
\n" ); document.write( "\n" ); document.write( "If the discriminant in the quadratic formula is a perfect square, then the quadratic equation will have __________________solution\r
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Algebra.Com's Answer #359052 by KMST(5328) $\"\"$ $\"About$

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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 $\"sqrt%28x%29=5\"$ to $\"x=5%5E2\"$ by squaring both sides, you are adding the extraneous solution $\"x=-5\"$ . (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).
\n" ); document.write( "2) The discriminant in the quadratic formula is the expression $\"b%5E2-4ac\"$ , which you see under the square root in the quadratic formula.
\n" ); document.write( "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. \n" ); document.write( "

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