part 1)
Use the quadratic formula to solve the equation.
4x^2−10x+5=0
we know that
the quadratic formula is
[tex]x=[-b (+/-) \sqrt{b^{2} -4ac}]/ 2a[/tex]
in this problem
a=4
b=-10
c=5
[tex]x=[10 (+/-) \sqrt{10^{2} -4*(4)*(5)}]/(2*4)\\ x=[10(+/-) \sqrt{20}]/8 \\ x1=[10+ \sqrt{20}]/8 \\ x2=(10- \sqrt{20}]/8 [/tex]
the answer Part 1) is
[tex]x1=(5+ \sqrt{5})/4 \\ x2=(5- \sqrt{5} )/4[/tex]
Part 2)
What are the zeros of the function f(x) =x^2+7x−18?
we have
f(x)=x²+7x-18
equals to zero the function
x²+7x-18=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
x²+7x=18
Complete
the square. Remember to balance the equation by adding the same constants
to each side
x²+7x+12.25=18+12.25
Rewrite as perfect squares
(x+3.5)²=30.25-----> square root----> (+/-)[x+3.5]=5.5
(+)[x+3.5]=5.5---> x=5.5-3.5----> x=2
(-)[x+3.5]=5.5----> x=-9
the answer part 2) is
the zero of the function are
x=2 and x=-9
Part 3) question of the picture
[tex](2 x^{2} +4x-8)-(4 x^{2} -x+1) \\ (2 x^{2} -4 x^{2} )+(4x+x)+(-8-1) \\ -2 x^{2} +5x-9 \\ standart form \\ a x^{2} +bx+c=0 \\ -2 x^{2} +5x-9=0[/tex]
