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Free_Kalibri [48]
3 years ago
12

F(x) = 4x² – 17x+3

Mathematics
1 answer:
Svet_ta [14]3 years ago
8 0

Answer:

discriminant: 241

2 real roots

Step-by-step explanation:

The discriminant is the part of the quadratic equation that is under the sqare root

x=(-b±√(b²-4ac))/2a

discriminant: b²-4ac

We also know that a quadratic equation is in the form ax²+bx+c = 0, so we can plug in the values we know from our equation to find the discriminant.

a=4

b=-17

c=3

(-17)^2-4(4)(3)

We also know that if the discriminant

is positive we have 2 real roots

is 0 we have 1 real root aka a repeated real solution

is negative we have no real roots

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What is the completely factored form of f(x)=x^3-7x^2+2x+4
xxMikexx [17]

Solution, \mathrm{Factor}\:x^3-7x^2+2x+4:\quad \left(x-1\right)\left(x^2-6x-4\right)

Steps:

x^3-7x^2+2x+4

Use\:the\:rational\:root\:theorem,\\a_0=4,\:\quad a_n=1,\\\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:4,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\\\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:4}{1},\\\frac{1}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x-1,\\\left(x-1\right)\frac{x^3-7x^2+2x+4}{x-1}

\frac{x^3-7x^2+2x+4}{x-1}

\mathrm{Divide}\:\frac{x^3-7x^2+2x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}x^3-7x^2+2x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{x^3}{x},\\\mathrm{Quotient}=x^2,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}x^2:\:x^3-x^2,\\\mathrm{Subtract\:}x^3-x^2\mathrm{\:from\:}x^3-7x^2+2x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=-6x^2+2x+4,\\Therefore,\\\frac{x^3-7x^2+2x+4}{x-1}=x^2+\frac{-6x^2+2x+4}{x-1}

\mathrm{Divide}\:\frac{-6x^2+2x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}-6x^2+2x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{-6x^2}{x}=-6x,\\\mathrm{Quotient}=-6x,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}-6x:\:-6x^2+6x,\\\mathrm{Subtract\:}-6x^2+6x\mathrm{\:from\:}-6x^2+2x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=-4x+4,\\\mathrm{Therefore},\\\frac{-6x^2+2x+4}{x-1}=-6x+\frac{-4x+4}{x-1}

\mathrm{Divide}\:\frac{-4x+4}{x-1},\\\mathrm{Divide\:the\:leading\:coefficients\:of\:the\:numerator\:}-4x+4\mathrm{\:and\:the\:divisor\:}x-1\mathrm{\::\:}\frac{-4x}{x}=-4,\\\mathrm{Quotient}=-4,\\\mathrm{Multiply\:}x-1\mathrm{\:by\:}-4:\:-4x+4,\\\mathrm{Subtract\:}-4x+4\mathrm{\:from\:}-4x+4\mathrm{\:to\:get\:new\:remainder},\\\mathrm{Remainder}=0,\\\mathrm{Therefore},\\\frac{-4x+4}{x-1}=-4

\mathrm{The\:Correct\:Answer\:is\:\left(x-1\right)\left(x^2-6x-4\right)}

\mathrm{Hope\:This\:Helps!!!}

\mathrm{-Austint1414}

8 0
3 years ago
What’s the answer For E
Vika [28.1K]

Answer:

∠E = 146°

Step-by-step explanation:

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∠E = 146°

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Answer:

10.5

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Yes, hope this helps
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1. Harsha makes a scale drawing of a window. She uses the scale 1cm represents 20cm.
guajiro [1.7K]

Part (A)

(1 cm)/(20 cm) = (6 cm)/(x cm)

1/20 = 6/x

1*x = 20*6

x = 120

120 cm = 120/100 = 1.2 m

<h3>Answer:  1.2 m</h3>

=========================================================

Part (B)

2.2 m = 2.2*100 = 220 cm

(1 cm)/(20 cm) = (x cm)/(220 cm)

1/20 = x/220

1*220 = 20*x

20x = 220

x = 220/20

x = 11

<h3>Answer: 11 cm</h3>
6 0
2 years ago
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