Question

Any one know how to find the roots of an equation?



A. 1/4 ± Square root of 10
B. 2/4 ± (i Square root of 10)/4
C. 1 ± (i Square root of 14)/2

i would like to know HOW to solve this problem.

Answer 1

so what you do is
make into ax^2+bx+c=0 form

add-9/2 to both sides
y^2-2y+9/2=0
now we use the quadratice formula which is
x=$\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

ax^2+bx+c=0
1y^2-2y+9/2
a=1
b=-2
c=9/2
subsitute
x=$\frac{-(-2)+/- \sqrt{(-2)^{2}-4(1)(9/2)} }{2(1)}$
x=$\frac{2+/- \sqrt{4-(36/2)} }{2}$
x=$\frac{2+/- \sqrt{4-(18)} }{2}$
x=$\frac{2+/- \sqrt{-14} }{2}$
x=$\frac{2+/- \sqrt{-14} }{2}$
x=$1+/- \frac{\sqrt{-14} }{2}$
x=$1+/- \frac{\sqrt{14} \sqrt{-1}}{2}$
x=$1+/- \frac{\sqrt{14} i }{2}$
x=$1+/- \frac{ i \sqrt{14} }{2}$

answer is C