Answer:
x^2 -6x + 222/25
Step-by-step explanation:
If the zeros are as above, then ;
x = 3-√3/5 or x = 3 + √3/5
Firstly, let’s represent √3/5 by b
Thus;
The two roots are ;
x = 3-b or x = 3 + b
so;
x+ b -3 and x -3-b
The quadratic equation is the product of the two
(x + b-3)(x - b -3)
x(x - b-3) + b(x -b -3) -3(x - b -3)
= x^2 -bx -3x + bx -b^2 -3b -3x + 3b + 9
Collect like terms and we are left with;
x^2 -6x -b^2 + 9
So let’s put back b = √3/5
x^2 -6x -(√3/5)^2 + 9
x^2 -6x -3/25 + 9
x^2 -6x + 222/25
cos (2x) = cos x
2 cos^2 x -1 = cos x using the double angle formula
2 cos ^2 x -cos x -1 =0
factor
(2 cos x+1) ( cos x -1) = 0
using the zero product property
2 cos x+1 =0 cos x -1 =0
2 cos x = -1 cos x =1
cos x = -1/2 cos x=1
taking the arccos of each side
arccos cos x = arccos (-1/2) arccos cos x = arccos 1
x = 120 degrees x=-120 degrees x=0
remember you get 2 values ( 2nd and 3rd quadrant)
these are the principal values
now we need to add 360
x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer
4/50 as a decimal is .08
Divide 4 by 50
