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4x^2+12x+10 ? I must show if this expression is positive. Please help me.

 May 2, 2015

Best Answer 

 #1
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First you must prove that this polynomial has no real roots.

(For any polynomial ax²+bx+c, the roots are $$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$)

If it doesn't have real roots, it will always have the same sign as a, which is 4 in that case. 4 is positive, so the polynomial is positive for any real number x.)

 May 2, 2015
 #1
avatar+870 
+5
Best Answer

First you must prove that this polynomial has no real roots.

(For any polynomial ax²+bx+c, the roots are $$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$)

If it doesn't have real roots, it will always have the same sign as a, which is 4 in that case. 4 is positive, so the polynomial is positive for any real number x.)

EinsteinJr May 2, 2015

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