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crimeas [40]
3 years ago
5

A root of x2 – 5x – 1 = 0 is

Mathematics
2 answers:
yan [13]3 years ago
8 0
x^2-5x-1=0\\\\
a=1,\ b=-5,\ c=-1\\\\
\Delta=b^2-4ac=(-5)^2-4*1*(-1)=25+4=29\\\\
\sqrt{\Delta}=\sqrt{29}\\\\
x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{29}}{2*1}=\frac{5-\sqrt{29}}{2}\\\\
x_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{29}}{2*1}=\frac{5+\sqrt{29}}{2}\\

Natasha2012 [34]3 years ago
8 0

<em><u>Answer:</u></em>

The roots are \frac{5+\sqrt{29}}{2} and \frac{5-\sqrt{29}}{2}

<em><u>Explanation:</u></em>

<u>The general form of the quadratic equation is:</u>

ax² + bx + c = 0

<u>The given equation is:</u>

x² - 5x - 1 = 0

<u>By comparison:</u>

a = 1

b = -5

c = -1

To get the roots of the equation, we will use the quadratic formula shown in the attached image.

<u>This means that:</u>

either x = \frac{5+\sqrt{(-5)^2-4(1)(-1)}}{2(1)}  = \frac{5+\sqrt{29}}{2}

or x = \frac{5-\sqrt{(-5)^2-4(1)(-1)}}{2(1)}  = \frac{5-\sqrt{29}}{2}

Hope this helps :)

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Find the length of LM if L is the midpoint of NM. NL = 3x + 1, LM = 8x - 24.
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Answer:

LM = 16

Step-by-step explanation:

From the question given:

L is the midpoint of NM

NL = 3x + 1

LM = 8x - 24

LM =?

Next, we shall determine the value of x.

This can be obtained as follow:

Since L is the midpoint of NM, it means that NL and LM are equal i.e

NL = LM

Thus, we can obtain the value of x as follow:

NL = 3x + 1

LM = 8x - 24

NL = LM

3x + 1 = 8x - 24

Collect like terms

3x - 8x = - 24 - 1

-5x = - 25

Divide both side by - 5

x = -25/-5

x = 5

Finally, we shall determine the length of LM as follow:

LM = 8x - 24

x = 5

LM = 8(5) - 24

LM = 40 - 24

LM = 16

Therefore, the length of LM is 16

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Use the equation and type the ordered-pairs. y = log 3 x {(1/3, a0), (1, a1), (3, a2), (9, a3), (27, a4), (81, a5)
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Answer:

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So the ordered pair will be (\frac{1}{3}, -1 )

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x=1

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So the ordered pair will be (1, 0 )

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So the ordered pair will be (27, 3 )

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y=a_{5}

y = log_{3}x\\y = log_{3}81\\y=4\log _3\left(3\right)\\y=4

So the ordered pair will be (81, 4 )

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