Question

Calculate the discriminant and use it to determine how many real-number roots the equation has.



3x2 – 6x + 4 = 0

Answer 1

A.
two real-number roots


B.
one real-number root


C.
three real-number roots


D.
no real-number roots

Answer 2

\(\bf {\color{brown}{ 3}}x^2 {\color{blue}{-6}}x{\color{olive}{ +4}} = 0\qquad discriminant\implies {\color{blue}{ b}}^2-4{\color{brown}{ a}}{\color{olive}{ c}}\)

Answer 3

Thanks for the Color :P

Answer 4

-36-4*12?

Answer 5

\(\bf (-6)^2-(4\cdot 3\cdot 4)\implies 36-48\)

Answer 6

So -12

Answer 7

so the discriminant is negative, meaning the roots will be complex ones both
because if you take root of -12, is an "imaginary" value, thus a complex number

Answer 8

But how do I find out how many real number roots are there?

Answer 9

well, is a quadratic equation, meaning degree is "2"
recall the fundamental theorem
thus roots are 2

if the discriminant is negative, you only have two complex solution, and no real ones

Answer 10

Oh, thanks Jdoe

Answer 11

yw