Find the discriminant and solutions for the following equations.
#1) 9x^2+6x+1=0
#2) -2x^2+3x-2+0
I will be happy to critique your work.
what is b^2-4ac?
#1) 9^2-4(6)(1)=
81-4(6)=
81-24=57
so then 57 is the solution but what is the discriminant or is 57 the discriminant?
#2) -2^2-4(3)(-2)=
4-144= -140
Then -140 would that be the solution or the discriminant?
To find the discriminant of a quadratic equation in the form ax^2 + bx + c = 0, you use the formula b^2 - 4ac.
Let's go through the provided equations and calculate both the discriminant and the solutions:
#1) 9x^2 + 6x + 1 = 0
a = 9, b = 6, c = 1
To find the discriminant:
Discriminant = b^2 - 4ac
= (6)^2 - 4(9)(1)
= 36 - 36
= 0
The discriminant for this equation is 0.
To find the solutions:
Using the quadratic formula, x = (-b ± √(b^2 - 4ac))/(2a), we can substitute the values:
x = (-6 ± √(0))/(2*9)
x = (-6 ± 0)/(18)
x = -6/18
x = -1/3
The equation has one real solution, x = -1/3.
#2) -2x^2 + 3x - 2 = 0
a = -2, b = 3, c = -2
To find the discriminant:
Discriminant = b^2 - 4ac
= (3)^2 - 4(-2)(-2)
= 9 - 16
= -7
The discriminant for this equation is -7.
To find the solutions:
Using the quadratic formula, x = (-b ± √(b^2 - 4ac))/(2a), we can substitute the values:
x = (-3 ± √(-7))/(2*(-2))
x = (-3 ± √(-7))/(-4)
x = (-3 ± i√7)/(-4)
The equation has two complex solutions, x = (-3 + i√7)/(-4) and x = (-3 - i√7)/(-4).
In summary, for equation #1, the discriminant is 0 and the solution is x = -1/3. For equation #2, the discriminant is -7, and the solutions are x = (-3 + i√7)/(-4) and x = (-3 - i√7)/(-4).