Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Let's solve the quadratic equation step by step:
The given quadratic equation has the coefficients:
[tex]\[ a = 1, \, b = -6, \, c = 9 \][/tex]
The quadratic formula is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
1. Calculate the discriminant:
The discriminant (Δ) is given by:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
Substituting the values:
[tex]\[ \Delta = (-6)^2 - 4(1)(9) \][/tex]
[tex]\[ \Delta = 36 - 36 \][/tex]
[tex]\[ \Delta = 0 \][/tex]
2. Calculate the roots using the quadratic formula:
Since the discriminant is 0, there is exactly one unique solution (repeated root):
[tex]\[ x = \frac{-b \pm \sqrt{\Delta}}{2a} \][/tex]
Substituting the values:
[tex]\[ x = \frac{-(-6) \pm \sqrt{0}}{2(1)} \][/tex]
[tex]\[ x = \frac{6 \pm 0}{2} \][/tex]
[tex]\[ x = \frac{6}{2} \][/tex]
[tex]\[ x = 3 \][/tex]
Thus, the roots of the quadratic equation are:
[tex]\[ x = 3 \, \text{and} \, x = 3 \][/tex]
To summarize:
- The discriminant (Δ) is 0
- The solutions are [tex]\( x_1 = 3.0 \)[/tex] and [tex]\( x_2 = 3.0 \)[/tex]
These results confirm that the quadratic equation has one unique solution, repeated twice.
The given quadratic equation has the coefficients:
[tex]\[ a = 1, \, b = -6, \, c = 9 \][/tex]
The quadratic formula is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
1. Calculate the discriminant:
The discriminant (Δ) is given by:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
Substituting the values:
[tex]\[ \Delta = (-6)^2 - 4(1)(9) \][/tex]
[tex]\[ \Delta = 36 - 36 \][/tex]
[tex]\[ \Delta = 0 \][/tex]
2. Calculate the roots using the quadratic formula:
Since the discriminant is 0, there is exactly one unique solution (repeated root):
[tex]\[ x = \frac{-b \pm \sqrt{\Delta}}{2a} \][/tex]
Substituting the values:
[tex]\[ x = \frac{-(-6) \pm \sqrt{0}}{2(1)} \][/tex]
[tex]\[ x = \frac{6 \pm 0}{2} \][/tex]
[tex]\[ x = \frac{6}{2} \][/tex]
[tex]\[ x = 3 \][/tex]
Thus, the roots of the quadratic equation are:
[tex]\[ x = 3 \, \text{and} \, x = 3 \][/tex]
To summarize:
- The discriminant (Δ) is 0
- The solutions are [tex]\( x_1 = 3.0 \)[/tex] and [tex]\( x_2 = 3.0 \)[/tex]
These results confirm that the quadratic equation has one unique solution, repeated twice.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.