Chapter 2.6, Problem 2ES

Consider the following quadratic f(x)=x2−11x+1f(x)=x2−11x+1 with the roots αα and ββ. Suppose the new quadratic g(x)=x2+px+qg(x)=x2+px+q has the roots γ=α+βγ=α+β and δ=1α+1βδ=1α+1β.  Find the coefficients pp and qq of the new quadratic correct to 2 decimal places. Select one: not in the list p= 13.00, q =  13.00 p= - 22.00, q = 121.00 p= 22.00, q = 123.00 p= 0.00, q = 121.00

Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.   n=​4; i and 5i are​ zeros; f(−1)=104

Find a formula for the polynomial P(x)P(x) with degree 3 a root of multiplicity 2 at x=1x=1 a root of multiplicity 1 at x=−4x=-4 yy-intercept (0,−2.8)

In  the given equation as follows , determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001:- see the equation as follows

Find the quadratic polynomial g(x)=ax^2+bx+c which best fits the function f(x)=3^x at x=0 in the sense that g(0)=f(0), and g′(0)=f′(0)g′(0)=f′(0), and g′′(0)=f′′(0), and g″(0)=f″(0). TIA g(x)=_____

The first three Legendre polynomials are 1, x, and x2 - ½. Choose c so that the fourth polynomial x3 -ex is orthogonal to the first three. All integrals go from -1 to 1.

Find a polynomial with integer coefficients that satisfies the given conditions. T has degree 4, zeros i and 1 + i, and constant term 10. T(x) =

Is the function in f(x)=x/29+2/x a rational function? If so, write it in the form p(x)/q(x), the ratio of polynomials, where p(x) has leading coefficient 1, and p(x) and q(x) share no common factors.

The polynomial f(x)=x^4+6x^3+ax^2-54x+c has four real roots r1, r2, r3, r4 such that r1+r2 = 0 and r4 –r3 = 4. Find a and c.Vietas formula