Show that the general cubic equation y3 + by2 + cy + d = 0can be transformed into an equation of the form x3 + px + q = 0by using the substitution y = x - b3

Q: 9. Identify the vertex, the y-intercept and the x intercepts for the following quadratic equation y…

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Q: ve [No.5] -2 2 зах 9x²-6x+5

A: On solving this we will get

Q: 2. Let r, 2 be the roots of the equation 2x-6x+3=0, construct an equation whose roots and are rr3,…

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Q: Find the quadratic y=ax2+bx+c that best fits the data points (−2,−37),(−1,63),(0,−43),(1,−5),(2,2) .…

A: To find the quadratic equation that best fits the given data points, we need to solve for the…

Q: solve: y" - 3y" + 2y = e2x 1+ex

A: To solve the given differential equation :     y'''-3y''+2y=e2x1+ex We will use the method of…

Q: Sketch y=-3(x-1)^(2)(x+2), making sure to account for end behavior along with zeros and their…

A: y=-3(x-1)^(2)(x+2)

Q: Find the constants A, B and C such that: 2x^2+6x+5= (Ax+ B)^2+ C b. Determine the range of values of…

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Q: b) Plot the quadratic y=-2x² + 8x-8, where 0≤x≤ 4.

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Q: Determine the equation of a quadratic function given zeros x=4 and point (3, 2)

A: Equation of quadratic function is given by as y = a(x-p)(x-q) Where x,y = passing point p,q = roots…

Q: Find the characteristics equation of x²r+2xys+y²t

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Q: y³ (x + 2y) = C²y

A: The solution is given as

Q: Find the depressed cubic equations for x3 - 6x2 -24x + 64 = 0

A: Given, x3-6x2-24x+64=0                   .......1Here, a=1 , b=-6 , c=24 , d=64Put x…

Q: Find atleast 1 root for the equation 5x5 + 10x? = 3

A: Introduction: An equation can be described mathematically as a statement that proves the equality of…

Q: 2. Solve: z dy (6r + 1)y+ 3r² + 2y* = 0 dr

A: The given differential equation is (6x+1)y2dydx+3x2+2y3=0. Divide both sides of the given equation…

Q: Verify  (x+1)2= 2 (x-3) is a quadratic equation or not

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Q: Find the general solection y'+ 3ty-

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Q: Explain the steps to find x- and y- intercepts of an equation of the form Ax + By = C

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Q: In l-1x+11-In !2x + 31) +C (2)C1)-(3)(-1)

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Q: Determine the equation of the quadratic function that passes through (-3, 20) if its x-intercepts a…

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Q: b) Plot the quadratic y=-2x² + 8x-8, where 0 ≤ x ≤ 4.

A: y=-2x2+8x-8

Q: X^(2)-12x+35=0 quadratic equation using quadratic forma

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Q: Given H(a)=a4-3a^2-a+1, the domain is

A: The domain of a function is the set of all values of the variable for which the function is define.…