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Dima020 [189]
3 years ago
9

What is the solution set of x2 + 5x + 1 = 0?

Mathematics
1 answer:
DerKrebs [107]3 years ago
3 0

Answer:

\huge\boxed{\left\{-\dfrac{5+\sqrt{21}}{2};\ \dfrac{-5+\sqrt{21}}{2}\right\}}

Step-by-step explanation:

x^2+5x+1=0\\\\\text{Use the quadratic formula:}\\\\\text{For}\ ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\\text{if}\ \Delta < 0,\ \text{then the equation has no real solution}\\\text{if}\ \Delta=0,\ \text{then the equation has one real solution}\ x=\dfrac{-b}{2a}\\\text{if}\ \Delta>0,\ \text{then the equation has two real solution}\ x=\dfrac{-b\pm\sqrt{\Delta}}{2a}

\text{We have}\\\\a=1,\ b=5,\ c=1\\\\\Delta=5^2-4(1)(1)=25-4=21>0\\\\x=\dfrac{-5\pm\sqrt{21}}{2(1)}=\dfrac{-5\pm\sqrt{21}}{2}

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