Discriminant?

Question

The discriminant of the equation 2x^2 - x - 1 = 0 indicates that the equation has:

a. exactly one real solution
b. 2 distinct real solutions
c. 2 complex solutions
d. no solution

can anyone tell me what the answer is and how they got it. and what are discriminants? real/complex solutions?

Answer 1

the discriminate is an indication if the solution to the quadratic have roots that are either real or complex.

often the discriminate is denoted as delta (Δ) representing
Δ = b^2 -4ac

and if the general equation is
aX^2 +bX + c=0
then the solution is
X = [ -b ± sqrt( b^2 -4ac ) ] /2a
or
X = [ -b ± sqrt( Δ ) ] /2a

hence if
d =0 then there will be only one solution
X = -b/2a

if d>0
then ther ewill be 2 distinct real solutions
X= [ -b + sqrt( Δ ) ] /2a or X= [ -b - sqrt( Δ ) ] /2a

if d<0 then sqrt(d) must be a complex with i^2=-1
hence
X= [ -b + sqrt( Δ )i ] /2a or X= [ -b - sqrt( Δ )i ] /2a

there is always a solution to any quadractic
very rare it would not have one

Answer 2

The discriminant is b^2-4ac: where a is the coefficient for x^2, b is the coefficient for x and c is constant coefficient.
In this case, the discriminant is: 1^2+8=9. Whenever this quantity is positive, there will be two distinct zeros. When it is negative there will be two complex solutions, and when it is zero, there will be only 1 solution.

Answer 3

2 real distinct solution or
1 real and 1 complex solution
2 complex solution

Answer 4

either b or v use b squared minus 4ac