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Anton [14]
3 years ago
10

Find the discriminant and determine the nature of the roots to the quadratic equation

Mathematics
1 answer:
Katen [24]3 years ago
3 0
№17
x^{2} +6x-7=0 \\ D=6 ^{2} -4*(-7)=36+28=64=8 ^{2}  \\  \\  x_{1} = \frac{-6+8}{2} =1 \\  \\  x_{2} = \frac{-6-8}{2} =-7
Answer: x₁ = 1
               x₂ = - 7

№18
2 x^{2} -3x+4=3 \\ 2 x^{2} -3x+4-3=0 \\ 2 x^{2} -3x+1=0 \\  \\ D= -3 ^{2} -4*2=9-8=1 \\  \\  x_{1} = \frac{3+1}{2*2} = \frac{4}{4} =1 \\  \\  x_{2} = \frac{3-1}{2*2} = \frac{2}{4} =0.5
Answer: x₁ = 1
               x₂ = 0,5.

№19
2 x^{2} -4x-5=0 \\  D=-4 ^{2} -4*2*(-5)=16+40=56 \\  \\  x_{1}= \frac{4+ \sqrt{56} }{2*2}  = \frac{4}{4} + \sqrt{ \frac{56}{16} } =1+ \sqrt{3.5}  \\  \\  x_{2} = \frac{4- \sqrt{56} }{2*2} = \frac{4}{4} -  \sqrt{ \frac{56}{16} } =1- \sqrt{3.5} 

Answer: x₁ = 1 + √3.5
               x₂ = 1 - √3.5

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4 0
1 year ago
A sector of a circle of 7cm has an area of 44cm².calculate the angle of the sector,correct to the nearest degree π =22\7​
Hitman42 [59]

Answer:

\theta=102.85^{\circ}

Step-by-step explanation:

Given that,

The radius of circle, r = 7 cm

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We need to find the angle of the sector. The formula for the area of sector is given by :

A=\dfrac{\theta}{360}\pi r^2

Solve for \theta.

\theta=\dfrac{360A}{\pi r^2}\\\\\theta=\dfrac{360\times 44}{\dfrac{22}{7}\times 7^2}\\\\\theta=102.85^{\circ}

So, the angle of the sector is equal to 102.85^{\circ}.

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3 years ago
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Nikolay [14]

Answer:

Levene confidence intervals ( b )

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5 0
3 years ago
What are the roots of the equation?<br><br> x^2(6x−11)(7x−8)=0
trasher [3.6K]

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3 0
3 years ago
Read 2 more answers
Please help! (question in attachment)
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