Question

Find the value of the discriminant and describe the number and type of roots.

3x2 - 5x + 6 = 0


x2 + 5x + 6 = 0

x2 - 8x +16 = 0

6x2 -x - 12 = 0

3x2 - 8x + 2 = 0

those are supposed to be x squared.

Answer 1

these are the answers to choose from for each problem

D=289, two irrational roots
D=40, two irrational roots
D= 289, two rational roots
D=0, two complex roots
D=0, one double root
D= -47, 2 complex roots
D= 1, two rational roots

Answer 2

the discriminant is

\[\Delta = b^2 - 4ac\]

in your question you have a = 3, b = -5 and c = 6

just substitute and evaluate.

conditions for the discriminant

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

\[b^2 - 4ac = 0\] there are 2 equal or repeated roots.... this is the case of a perfect square.

\[b^2 - 4ac< 0\] there are no real roots.... there will be 2 unequal complex roots

Answer 3

wat does all that mean?