IDNLearn.com helps you find the answers you need quickly and efficiently. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.
Sagot :
Sure, let's solve the quadratic equation [tex]\(x^2 + 7x + 4 = 0\)[/tex] using the quadratic formula.
The quadratic formula is given by:
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \][/tex]
Here, the coefficients are [tex]\(a = 1\)[/tex], [tex]\(b = 7\)[/tex], and [tex]\(c = 4\)[/tex].
1. Calculate the discriminant:
[tex]\[ \text{Discriminant} = b^2 - 4ac = 7^2 - 4 \cdot 1 \cdot 4 = 49 - 16 = 33 \][/tex]
2. Apply the quadratic formula:
[tex]\[ x = \frac{{-b \pm \sqrt{{\text{Discriminant}}}}}{2a} = \frac{{-7 \pm \sqrt{33}}}{2 \cdot 1} = \frac{{-7 \pm \sqrt{33}}}{2} \][/tex]
Now, let's find the two solutions by separately considering the `plus` and `minus` parts of the formula:
- First solution ([tex]\(x_1\)[/tex]):
[tex]\[ x_1 = \frac{{-7 + \sqrt{33}}}{2} \][/tex]
- Second solution ([tex]\(x_2\)[/tex]):
[tex]\[ x_2 = \frac{{-7 - \sqrt{33}}}{2} \][/tex]
Putting it all together, the solutions to the quadratic equation [tex]\(x^2 + 7x + 4 = 0\)[/tex] are:
[tex]\[ x_1 = \frac{{-7 + \sqrt{33}}}{2} \quad \text{and} \quad x_2 = \frac{{-7 - \sqrt{33}}}{2} \][/tex]
These solutions are approximately [tex]\(-0.628\)[/tex] and [tex]\(-6.372\)[/tex], respectively.
So, the correct answer from the provided options is:
[tex]\[ x = \frac{{-7 \pm \sqrt{33}}}{2} \][/tex]
The quadratic formula is given by:
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \][/tex]
Here, the coefficients are [tex]\(a = 1\)[/tex], [tex]\(b = 7\)[/tex], and [tex]\(c = 4\)[/tex].
1. Calculate the discriminant:
[tex]\[ \text{Discriminant} = b^2 - 4ac = 7^2 - 4 \cdot 1 \cdot 4 = 49 - 16 = 33 \][/tex]
2. Apply the quadratic formula:
[tex]\[ x = \frac{{-b \pm \sqrt{{\text{Discriminant}}}}}{2a} = \frac{{-7 \pm \sqrt{33}}}{2 \cdot 1} = \frac{{-7 \pm \sqrt{33}}}{2} \][/tex]
Now, let's find the two solutions by separately considering the `plus` and `minus` parts of the formula:
- First solution ([tex]\(x_1\)[/tex]):
[tex]\[ x_1 = \frac{{-7 + \sqrt{33}}}{2} \][/tex]
- Second solution ([tex]\(x_2\)[/tex]):
[tex]\[ x_2 = \frac{{-7 - \sqrt{33}}}{2} \][/tex]
Putting it all together, the solutions to the quadratic equation [tex]\(x^2 + 7x + 4 = 0\)[/tex] are:
[tex]\[ x_1 = \frac{{-7 + \sqrt{33}}}{2} \quad \text{and} \quad x_2 = \frac{{-7 - \sqrt{33}}}{2} \][/tex]
These solutions are approximately [tex]\(-0.628\)[/tex] and [tex]\(-6.372\)[/tex], respectively.
So, the correct answer from the provided options is:
[tex]\[ x = \frac{{-7 \pm \sqrt{33}}}{2} \][/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.