Real Solutions for Quadratic Equation 5x^2+2x+1=0

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The quadratic equation 5x^2 + 2x + 1 = 0 has complex roots, as indicated by a negative discriminant when applying the quadratic formula. The correct formula to use is \(-b \pm \sqrt{b^2 - 4ac} / 2a\). The discussion highlights the importance of accurately using the quadratic formula to avoid confusion in future problems. It clarifies that the equation does not have real number roots, which was likely the intended focus of the question. Understanding these concepts is crucial for solving quadratic equations effectively.
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Homework Statement


5x^2+2x+1=0


Homework Equations


-b +- sqrt{b^2 +- 4ac}


The Attempt at a Solution


once applied the quadratic formula, i got a minus under the discrimant which means i received an error. any other recommendations on how to solve this baby?
 
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There's no error here if you copied the question correctly. The roots of this equation are complex.
 
The roots of this equation are complex, but you should be aware that the Quadratic Formula is not the one you typed: it is

<br /> \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}<br />

The version you have could cause you massive grief in the future.
 
yes sorry i ment that formula. So this equation has no roots(complex)
 
It has no real number roots which was the question (I think) you intended to pose.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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