4. Verify whether S(x) is a cubic spline x³ x - 1 S(x) = { ²² + ² 17²³ + 2(x − 1)² + 4(x − 1) + 1 − If not, how can it be fixed? Is the original function or its revision a natural cubic spline? Is it a not-a-knot cubic spline? on [0, 1) on [1,2]

Q: Prove that c = 4 is the largest root of f (x) = x4 − 8x2 − 128.

A: Given function is, fx=x4-8x2-128. To find the largest root substitute x4-8x2-128=0 Let x2=u. Then,…

Q: 5. Find a polynomial of degree 3 whose zeros are 4, 1,-2 and y intercept 16.

A: Since given that the polynomial has degree 3 and its zeros are 4, 1, and -2.Then the polynomial can…

Q: 1. Express the polynomial f(x) = 4x3 – 5x2 + 2x – 3 as a power of x + 2.

A:

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Q2 /| Find a cubic polynomial of x (5, 147). given points (0, 2), (1, 3), (2, 12),

A: Newton's divided differences interpolation

Q: Find the formula for the fourth degree polynomial containing the point (0,8) and whose graph is…

A: We have to find the equation for the given graph.

Q: 8. Find one zero of the polynomial f(x)=2x-x-6x+3 %3D

A: Given function is: Apply rational root theorem to get roots of polynomial. If the polynomial has a…

Q: A graph of y=f(x) is shown, where f(x)=2x^5-3x^4+x^3-8x^2+5x+3 and f(-x)= -2x^5-3x^4-x^3-8x^2-5x+3.…

A:

Q: The zeros of the polynomial function f(x)=x² – 2x² – 15x are: a. {-5,–3,0} . b. {-3,5} . c. {-5,3} .…

A: We have the given function as fx=x3-2x2-15x On solving further by making factors, we get the result…

Q: 2(×+2)^2-18=0 is the equation resulting from setting a quadratic fuction f(×) equal 0 and completing…

A: A parabola having axis of symmetry along y-axis or a line parallel to y-axis is given by…

Q: Given f(x) = - - 6x + 2, h(x) = 2(x – 6)(x+ 10) and g(x) =(x - 4)²+2 deter write f, g or h) has no…

A: Given,       f(x)=-34x2-6x+2h(x)=2(x-6)(x+10)g(x)=65(x-4)2+2

Q: 2. Let p(x) represent a 7th degree polynomial whose roots are √/2 and 1 (triple root) and it passes…

A: Given 1. px represents 7th degree polynomial 2. whose roots are 2 and 1 (triple root) 3. And it…

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

A:

Q: Let f(x)=x-x -x-2. Given that f(x) has a zero x = 2, find all real and imaginary zeros of the…

A: The zeros of the function can be calculated by long division. The long division reduces the function…

Q: 4. Find the remainder of f (x) = (1 + x)3/² of degree 3.

A:

Q: Find the lowest-degree polynomial that interpolates the function f(x) = 2x² - 1, in the nodes To =…

A: The Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a…

Q: 9. Find all real zeroes of the function p(x)=6x' +17x² – 26x +8

A: Definition used-              Rational zero theorem  -                       If a…

Q: a.) Calculate L6 for f(x)= (squareroot (9x+1)) over [1,3] Give answer to three decimal places L6=…

A:

Q: What are all the real zeroes of y=(x–12)^3 –7? Please show work. Thank you:)

A: Given: y = (x - 12)3 - 7 What are all the real zeros.

Q: 4. Prove that f(r) = 4x³ - 8² + 2x + 1 has three real zeros. %3D

A: