# SOLUTION: Please help me solve this: Given {{{ f(x)= 2(x-3)(x+2)^2+2(x+2)(x-3)^3 }}} show that {{{ x^2-5x+11>0 }}} for all integers x.

Algebra ->  Algebra  -> Equations -> SOLUTION: Please help me solve this: Given {{{ f(x)= 2(x-3)(x+2)^2+2(x+2)(x-3)^3 }}} show that {{{ x^2-5x+11>0 }}} for all integers x.      Log On

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 Algebra: Equations Solvers Lessons Answers archive Quiz In Depth

 Question 516980: Please help me solve this: Given show that for all integers x.Answer by richard1234(5390)   (Show Source): You can put this solution on YOUR website!The "given" part is rather pointless, because we can prove that statement for all integers x without it. The roots of the quadratic equation are: This is a complex number, so the quadratic has no real roots. This means that the function is either all positive or all negative. Since the x^2 coefficient is positive, the entire function must be positive (since it opens upward and a quadratic having any negative values would be bounded by the x-axis).