Sketch the picture graph of fx Let fx be linear Find fx f7

Sketch the picture graph of |f(x)| Let f(x) be linear Find: f(x) f(7) = 19 Calculate: f(25) f(1) = 43 Find 2 points on each of the following lines thoroughly line work out all any thoroughly but do not perform any calculations subtraction, other than addition, subtraction, on cancellation (if possible) in a function. y + 15/x - 4 = 11 + 15/9 - 4 y + 3/x + c = -13/9 y= -2/7 x + 6 8x - 3y = 48 Under the same conditions as a part (a) sketch the picture graph of 5x + 11y = 0 Find the lines {11 h} to the line 17x + 23y = 41 and the passing through the point (pi + 3 squareroot 2, 1/squareroot 5 - 4 squareroot 4). Do not work out any calculations. Graph the function: f(x) = (4 - 3x)^3 |6 - 11x|^2 (x)/-2x^4 |3x + 13 - 2 show all intercepts and asymptotes! Factor completely and find all the squareroots of: p(x) = x^4 + x^3 + x + 1 Show that the quadrilateral (4-sided figure) obtained of a given quadrilateral is a parallelogram opposite sides parallel

Solution

P(X) = x^4 + x^3 + x+ 1

according to rational roots test possible rational roots of the polynomial are

+1 , -1

on plugging x = -1 in the polynomial we get

(-1)^4 + (-1)^3 +(-1) +1 = 0

hence one root is -1

now to find other roots divide the polynomial p(x) by (x+1) ^2

(x^4 + x^3 + x+ 1) / (x+1)^2

on dividing we get

x^2+x+1

on solving x^2-x+1 we get

x = (1+sqrt 3 i )/2

x = (1- sqrt 3 i) / 2

hence there are 2 real roots and 2 complex roots for this polynomial

x1 = -1

x2 = -1

x3 = (1+sqrt 3 i )/2

x4 = (1-sqrt 3 i )/2