III. C4FM 1. 2. 3. 4. 5. Solve the following rational equations by following the steps. Check your answer for extraneous solution. x+6 3 x-2 4 3-x 6-x 6 12 x+3 16 X x-3 X 15 3x 2 3 1 2x 5 4 6 x+2 x-2 Checking: Checking: Checking: Checking:

Q: Show that x2 + 6 = 6x has a real solution between 3 and 6.

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Q: - 3. Given f(x) = 2x² − 3 and g(x) = 3x +1. Find f(-4), g(1/6), (fƒ+ g)(-1), (fƒ— g)(4). Solution:

A: Given f(x)=2x2-3 and g(x)=3x+1 We need to find f(-4) ,g(1/6) ,(f+g)(-1), (f-g)(4)

Q: For any real number xx the maximum value of 4−6a−a2 is, 4 7 9 13

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Q: Invent interesting and original positive integers a, b, and c. (a)Let p(x) = −4(x+a)(2x−b)(3x+c).…

A: Given p(x) = −4(x+a)(2x−b)(3x+c)q(x) = −3x + 5x − 2x + 10

Q: Determine the Values fx for which the funchion floo= $2x? -4 7x+2 x <2 26X<5 is dis continuous 7

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Q: x2 – 2r – 3 c(x) = x2 + 4x – 5 2. Fill the Table: 3. Graph the function:

A: Given that cx=x2-2x-3x2+4x-5  To plot the function and fill the table, we put some arbitrary values…

Q: 11 When 2x' + x² – 2kx + f is divided by x – 1, the remainder is -4, and when it is divided by x +…

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Q: n-1 Is (x – a) a factor of f(x) = x" + ax - 2a", where n is a whole number, n = {1, 2, 3,...}. Argue…

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Q: Determine whether x = (0 3 0 9 2) is a solution

A: Given that max   2x2+2x5s.tx1+x2-x5=1x2+x3+x5=5-2x2+x4+x5=5x1,x2, x3,x4, x5≥0 To determine…

Q: Maria 5x2-3x 2 b2- 4ac %3D (-3)2 - 4(5)(2) - -31 Since the discriminant is -31, there are no real…

A: The discriminant of the quadratic equation  ax2+bx+c=0 is: D=b2-4ac

Q: When x³ + x² - kx - 5 is divided by x - 2 the remainder is 1. Find the value of k.

A: Remainder Theorem:If a polynomial p(x) is divided by x-a then the remainder is p(a)

Q: Which of these is not an appröprlate st in factoring f (x)= 4x? – 3zy + 20z – 15y? 4a2 + 20x – 3ay –…

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Q: maximise 2.01 + *2 subject to T1 – X2 < 1, 2x1- x2 1, 2x1 + 2x2 2 4, X1, X2 20

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Q: pð – xª + 4x3 – 4x² + 8x – 4 d.x - - (x² + 4)²

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Q: Solve the following rational equation. You MUST show work for full credit. 小=

A: The given rational equation,1) xx-3=232) x+33=8x-2

Q: If when P(x) is divided by (x + 2), the quotient is (6x – 7) and the remainder is -60, then…

A: given that when P(x) is divided by (x+2) then  the quotient is (6x-7) and the  remainder is -60.  so…

Q: - 3. Given ƒ(x) = 2x² − 3 and g(x) = 3x +1. Find ƒ (-4), g(1/6), (f+g)(-1), (fƒ— g)(4). Solution:

A: Given, f(x) = 2x2-3  and  g(x) = 3x+1  We have to find f(-4), g(1/6), (f + g)(-1), (f - g)(4).

Q: You may find the following useful: The polynomial 3x + 12r + 11 = 0 has the solutions r = -2.58 and…

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Q: √2. y=x² - 4x and y=-x² + 2x.

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Q: Identify the zeros and multiplicity for p(x) = 2x(x + 3)5(2x - 7)³. Show your work for identifying…

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