Question

Write the value of the discriminant of each equation. Then use it to decide how many different real-number root the equation has. (do not solve.)

x^2-3x+2

Answer 1

the discriminant is the "under the square root" stuff in the quadratic formula. \[\sqrt{b^2-4ac}\]

Answer 2

What I don't get is, when I put it into the discriminant: it becomes 9-8... which is 1.. and I have no idea where that goes or what proves what.

Answer 3

ok. yeah

Answer 4

HAHA. :)

Answer 5

it is =1. this tells you how many roots you have. \[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]If the discriminant is negative, you have no solutions/root (cant square root a negative number). If the discriminant is =0, the you have one real solution. If it is positive, you have two real roots.

Answer 6

OHHHHHH I SEEEE HAAHHAHAHAHH
what i DIDN'T know was you had to plug it into the quaratic formula. now I see!
so ... I have 2 real solutions right?

Answer 7

the conditions for the discriminant are

\[b^2 - 4ac > 0\] two unequal real roots...if its a perfect square the roots are rational if not irrational

\[b^2 - 4ac = 0\] 2 equal real roots.... this is the perfect square case (x + b)^2 = 0

\[b^2 - 4ac < 0\] two inequal complex roots.... or they made be described as no real roots.

Answer 8

so.... i'm right right?..

Answer 9

yep; 2 roots.

Answer 10

technically cambell st is correct with the =0 case. I always say one real root but it is actually 2 equal real roots when discriminant =0.

Answer 11

haah thanks :D