Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To find the roots of the quadratic equation [tex]\(2x^2 + 8x + 7 = 0\)[/tex], we can use the quadratic formula, which is given by:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Here, the coefficients are [tex]\(a = 2\)[/tex], [tex]\(b = 8\)[/tex], and [tex]\(c = 7\)[/tex].
First, we need to calculate the discriminant, which is [tex]\(b^2 - 4ac\)[/tex]:
[tex]\[ \text{Discriminant} = b^2 - 4ac = 8^2 - 4 \cdot 2 \cdot 7 = 64 - 56 = 8 \][/tex]
So, the discriminant is [tex]\(8\)[/tex].
Next, we use the quadratic formula to find the roots:
[tex]\[ x = \frac{-b \pm \sqrt{\text{Discriminant}}}{2a} = \frac{-8 \pm \sqrt{8}}{2 \cdot 2} = \frac{-8 \pm \sqrt{8}}{4} \][/tex]
Let's simplify [tex]\(\sqrt{8}\)[/tex]:
[tex]\[ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} \][/tex]
Now, we substitute [tex]\(\sqrt{8}\)[/tex] with [tex]\(2\sqrt{2}\)[/tex] in the quadratic formula:
[tex]\[ x = \frac{-8 \pm 2\sqrt{2}}{4} = \frac{-8}{4} \pm \frac{2\sqrt{2}}{4} = -2 \pm \frac{\sqrt{2}}{2} \][/tex]
Upon further simplification:
[tex]\[ x = -2 \pm \frac{\sqrt{2}}{2} \][/tex]
This gives us two roots:
[tex]\[ x_1 = -2 + \frac{\sqrt{2}}{2} \][/tex]
And
[tex]\[ x_2 = -2 - \frac{\sqrt{2}}{2} \][/tex]
From the given options, the correct answer matches the simplified form:
D. [tex]\( x = \frac{-2 \pm \sqrt{2}}{1} \)[/tex]
Hence, the correct answer is:
D. [tex]\(x = \frac{-2 \pm \sqrt{2}}{1}\)[/tex]
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Here, the coefficients are [tex]\(a = 2\)[/tex], [tex]\(b = 8\)[/tex], and [tex]\(c = 7\)[/tex].
First, we need to calculate the discriminant, which is [tex]\(b^2 - 4ac\)[/tex]:
[tex]\[ \text{Discriminant} = b^2 - 4ac = 8^2 - 4 \cdot 2 \cdot 7 = 64 - 56 = 8 \][/tex]
So, the discriminant is [tex]\(8\)[/tex].
Next, we use the quadratic formula to find the roots:
[tex]\[ x = \frac{-b \pm \sqrt{\text{Discriminant}}}{2a} = \frac{-8 \pm \sqrt{8}}{2 \cdot 2} = \frac{-8 \pm \sqrt{8}}{4} \][/tex]
Let's simplify [tex]\(\sqrt{8}\)[/tex]:
[tex]\[ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} \][/tex]
Now, we substitute [tex]\(\sqrt{8}\)[/tex] with [tex]\(2\sqrt{2}\)[/tex] in the quadratic formula:
[tex]\[ x = \frac{-8 \pm 2\sqrt{2}}{4} = \frac{-8}{4} \pm \frac{2\sqrt{2}}{4} = -2 \pm \frac{\sqrt{2}}{2} \][/tex]
Upon further simplification:
[tex]\[ x = -2 \pm \frac{\sqrt{2}}{2} \][/tex]
This gives us two roots:
[tex]\[ x_1 = -2 + \frac{\sqrt{2}}{2} \][/tex]
And
[tex]\[ x_2 = -2 - \frac{\sqrt{2}}{2} \][/tex]
From the given options, the correct answer matches the simplified form:
D. [tex]\( x = \frac{-2 \pm \sqrt{2}}{1} \)[/tex]
Hence, the correct answer is:
D. [tex]\(x = \frac{-2 \pm \sqrt{2}}{1}\)[/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.