A. the radicand is b²-4ac if it is in form ax²+bx+c
when it is greater than 0, then 2 real roots equal to 0, then 1 real root less than 0, then no real roots
so a=4 b=-12 c=10
b²-4ac=(-12)²-4(4)(10)=144-160<0 so 0 real roots
B. using quadratic formula because it is easier for ax²+bx+c=0 [tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
so
for 2x²-13x+21 a=2 b=-13 c=21
[tex]x=\frac{-(-13)+/-\sqrt{(-13)^2-4(2)(21)}}{2(2)}[/tex] [tex]x=\frac{13+/-\sqrt{169-168}}{4}[/tex] [tex]x=\frac{13+/-\sqrt{1}}{4}[/tex] [tex]x=\frac{13+/-1}{4}[/tex] x=(13+1)/4 or (13-1)/4 x=14/4 or 12/4 x=7/2 or 3
