1 Find the equation whose roots are each two more than the r

1.    Find the equation whose roots are each two more than the roots of x³-4x²+3x-2=0.

2.    If 2 is a root of the equation 2x³-5kx²+7x+10=0, find the value of k.

3.    What polynomial is multiplied by x² -4x-21 to give you x³-6x²-13x+42?

4.    For the function g(x)=-2x³(x-2)².

a) State the degree of the function and comment on its end behavior.

b) State the zeros.

5.a) The function y=f(x)= x⁴ is translated 2 units to the left and 3 units up. (express domain and range.)

b) The function y=f(x)=x⁵ is stretched horizontally by a factor of 7 and translated 2 units to the right. (express domain and range.)

c) The function y=f(x)= x³ is stretched vertically by a factor of 4, reflected in the y-axis, and translated 3 units up and 5 units to the left. (express domain and range.)

** The questions I want to be answered most are 1 and 2. The others aren\'t required from you, although if you are able to do them that would be a great help...your kind assistance is greatly appreciated.

Solution

1) Given equation is x^3 - 4x^2 + 3x - 2 = 0.

The roots of the equation are x = 3.3, (0.365 + i* 0.7),  (0.365 - i* 0.7)

Now make all two more:

x1 = 3.3 + 2 = 5.3

x2 = (2.365 + i* 0.7)

x3 = (2.365 - i* 0.7)

Find the equation using roots:

(x - x1)(x - x2)(x - x3) = (x - 5.3)(x - 2.365 - i* 0.7)(x - 2.365 + i* 0.7)

= (x - 5.3)(x^2 - 4.73x + 6.08) = x^3 - 10.03x^2 + 31.149x - 32.224