SOLUTION: determine whether the equation has 2 solutions, 1 solution, or no solution. SHOW WORK! PUT IN STANDARD FORM! 22)x^2-3x+2=0 24)-3x^2+5x-1=0 26)x^2-2x+4=0 28)3x^2-6x+3=0 30

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#22

From the quadratic formula


the discriminant consists of all of the terms in the square root. So the discriminant is



the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.


Now let's find the discriminant for :

Plug in a=1, b=-3, c=2

Square -3 to get 9

Multiply -4*1*2 to get -8

Combine 9 and -8 to get 1


Since the discriminant equals 1 (which is greater than zero) , this means there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.

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#24


From the quadratic formula


the discriminant consists of all of the terms in the square root. So the discriminant is



the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.


Now let's find the discriminant for :

Plug in a=-3, b=5, c=-1

Square 5 to get 25

Multiply -4*-3*-1 to get -12

Combine 25 and -12 to get 13


Since the discriminant equals 13 (which is greater than zero) , this means there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.