Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To solve the quadratic equation [tex]\(2x^2 + x - 4 = 0\)[/tex], we will use the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Here, the coefficients are:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 1 \)[/tex]
- [tex]\( c = -4 \)[/tex]
Firstly, we need to calculate the discriminant, which is given by [tex]\( b^2 - 4ac \)[/tex]:
[tex]\[ \text{Discriminant} = b^2 - 4ac \][/tex]
Substituting the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[ \text{Discriminant} = 1^2 - 4 \cdot 2 \cdot (-4) \][/tex]
[tex]\[ \text{Discriminant} = 1 + 32 \][/tex]
[tex]\[ \text{Discriminant} = 33 \][/tex]
The discriminant is 33.
Now, we apply these values into the quadratic formula to find the two solutions for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-1 \pm \sqrt{33}}{2 \cdot 2} \][/tex]
[tex]\[ x = \frac{-1 \pm \sqrt{33}}{4} \][/tex]
This yields two solutions:
[tex]\[ x_1 = \frac{-1 + \sqrt{33}}{4} \][/tex]
[tex]\[ x_2 = \frac{-1 - \sqrt{33}}{4} \][/tex]
Approximating the values:
[tex]\[ x_1 \approx 1.186 \][/tex]
[tex]\[ x_2 \approx -1.686 \][/tex]
So, the solutions to the quadratic equation [tex]\(2x^2 + x - 4 = 0\)[/tex] are approximately:
[tex]\[ x_1 \approx 1.186 \][/tex]
[tex]\[ x_2 \approx -1.686 \][/tex]
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Here, the coefficients are:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 1 \)[/tex]
- [tex]\( c = -4 \)[/tex]
Firstly, we need to calculate the discriminant, which is given by [tex]\( b^2 - 4ac \)[/tex]:
[tex]\[ \text{Discriminant} = b^2 - 4ac \][/tex]
Substituting the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[ \text{Discriminant} = 1^2 - 4 \cdot 2 \cdot (-4) \][/tex]
[tex]\[ \text{Discriminant} = 1 + 32 \][/tex]
[tex]\[ \text{Discriminant} = 33 \][/tex]
The discriminant is 33.
Now, we apply these values into the quadratic formula to find the two solutions for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-1 \pm \sqrt{33}}{2 \cdot 2} \][/tex]
[tex]\[ x = \frac{-1 \pm \sqrt{33}}{4} \][/tex]
This yields two solutions:
[tex]\[ x_1 = \frac{-1 + \sqrt{33}}{4} \][/tex]
[tex]\[ x_2 = \frac{-1 - \sqrt{33}}{4} \][/tex]
Approximating the values:
[tex]\[ x_1 \approx 1.186 \][/tex]
[tex]\[ x_2 \approx -1.686 \][/tex]
So, the solutions to the quadratic equation [tex]\(2x^2 + x - 4 = 0\)[/tex] are approximately:
[tex]\[ x_1 \approx 1.186 \][/tex]
[tex]\[ x_2 \approx -1.686 \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.