document.write( "Question 1144405: Find all values of h for which the quadratic equation has two real solutions. 3x^2+7x +h=0. Write your answer as an equality or inequality in terms of h. \n" ); document.write( "
Algebra.Com's Answer #765515 by MathTherapy(10552)\"\" \"About 
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Find all values of h for which the quadratic equation has two real solutions. 3x^2+7x +h=0. Write your answer as an equality or inequality in terms of h.
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When the DISCRIMINANT (b2  -  4ac) > 0, and is a PERFECT SQUARE, then the ROOTS are REAL, RATIONAL and UNEQUAL.
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document.write( "When the DISCRIMINANT (b2  -  4ac) > 0, and is a NON-PERFECT SQUARE, then the ROOTS are REAL, IRRATIONAL and UNEQUAL.
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document.write( "When the DISCRIMINANT (b2  -  4ac) = 0, then the ROOTS are REAL, RATIONAL and EQUAL.
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document.write( "Therefore, in this case, since you need TWO (2) REAL solutions, then I'd say that, with the DISCRIMINANT \"b%5E2++-++4ac+%3E=+0\", and the equation, \"3x%5E2+%2B+7x+%2B+h+=+0\", we get:
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document.write( "\"7%5E2+-+4%283%29%28h%29+%3E=+0\"
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document.write( "\"49+-+12h+%3E=+0\"
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document.write( "\"-+12h+%3E=+-+49\"
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document.write( "\"matrix%281%2C3%2C+h+%3C=+%28-+49%29%2F%28-+12%29%2C+%22======%3E%22%2C+h+%3C=+49%2F12%29\" \n" );
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