Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. x^2=3x-6
x^2=3x-6
x^2-3x+6=0
In quadratic equation y=ax^2+bx+c
discriminate is D=b^2-4ac
In your case a=1 b= -3 c=6
D=b^2-4ac=(-3)^2-4*1*6=9-24= -15
When discriminante is negative quadratic have two imaginare solutions.
If you want to know that solutions in google type:
quadratic equation online
When you see list of results click on:
webgraphingcom/quadraticequation_quadraticformula.jsp
When page be open in rectacangle type:
x^2-3x+6=0
and click option solve it
You will see solution step-by-step
To determine the nature of the solutions for the equation x^2 = 3x - 6 using the discriminant, we need to calculate the discriminant first.
The quadratic equation x^2 - 3x + 6 = 0 is in the standard form ax^2 + bx + c = 0, where a = 1, b = -3, and c = 6.
The discriminant (D) is given by the formula: D = b^2 - 4ac.
Substituting the values for a, b, and c into the formula, we have:
D = (-3)^2 - 4(1)(6)
= 9 - 24
= -15
The value of the discriminant is -15.
Now, we can determine the nature of the solutions based on the value of the discriminant:
1. If the discriminant (D) is positive (D > 0), the quadratic equation has two different rational solutions.
2. If the discriminant (D) is zero (D = 0), the quadratic equation has exactly one rational solution.
3. If the discriminant (D) is negative (D < 0), the quadratic equation has two different imaginary solutions.
4. If the discriminant (D) is a perfect square negative number, the quadratic equation has two different irrational solutions.
In our case, the discriminant (-15) is negative (D < 0). Therefore, the equation x^2 = 3x - 6 has two different imaginary solutions.