Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To solve this problem, we will start by comparing the given quadratic formula application to the standard form of a quadratic equation. The standard form of a quadratic equation is:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
We are given the quadratic formula:
[tex]\[ x = \frac{-8 \pm \sqrt{8^2 - 4(3)(-2)}}{2(3)} \][/tex]
From this formula, we can deduce the coefficients:
[tex]\[ a = 3 \][/tex]
[tex]\[ b = 8 \][/tex]
[tex]\[ c = -2 \][/tex]
Next, we need to match this to one of the given equations. Let's examine each option to see if it matches the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex] when rearranged.
### Option A: [tex]\(-2x^2 - 8 = 10x - 3\)[/tex]
Rearranging the terms to standard form:
[tex]\[ -2x^2 - 8 = 10x - 3 \\ -2x^2 - 10x - 8 + 3 = 0 \\ -2x^2 - 10x - 5 = 0 \][/tex]
This does not match the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex].
### Option B: [tex]\(3x^2 - 8x - 10 = 4\)[/tex]
Rearranging the terms to standard form:
[tex]\[ 3x^2 - 8x - 10 = 4 \\ 3x^2 - 8x - 10 - 4 = 0 \\ 3x^2 - 8x - 14 = 0 \][/tex]
This does not match the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex].
### Option C: [tex]\(3x^2 + 8x - 10 = -8\)[/tex]
Rearranging the terms to standard form:
[tex]\[ 3x^2 + 8x - 10 = -8 \\ 3x^2 + 8x - 10 + 8 = 0 \\ 3x^2 + 8x - 2 = 0 \][/tex]
This matches the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex].
### Option D: [tex]\(-2x^2 + 8x - 3 = 4\)[/tex]
Rearranging the terms to standard form:
[tex]\[ -2x^2 + 8x - 3 = 4 \\ -2x^2 + 8x - 3 - 4 = 0 \\ -2x^2 + 8x - 7 = 0 \][/tex]
This does not match the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex].
Thus, the only equation that matches the given standard form is option:
[tex]\[ C: 3x^2 + 8x - 10 = -8 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
[tex]\[ ax^2 + bx + c = 0 \][/tex]
We are given the quadratic formula:
[tex]\[ x = \frac{-8 \pm \sqrt{8^2 - 4(3)(-2)}}{2(3)} \][/tex]
From this formula, we can deduce the coefficients:
[tex]\[ a = 3 \][/tex]
[tex]\[ b = 8 \][/tex]
[tex]\[ c = -2 \][/tex]
Next, we need to match this to one of the given equations. Let's examine each option to see if it matches the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex] when rearranged.
### Option A: [tex]\(-2x^2 - 8 = 10x - 3\)[/tex]
Rearranging the terms to standard form:
[tex]\[ -2x^2 - 8 = 10x - 3 \\ -2x^2 - 10x - 8 + 3 = 0 \\ -2x^2 - 10x - 5 = 0 \][/tex]
This does not match the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex].
### Option B: [tex]\(3x^2 - 8x - 10 = 4\)[/tex]
Rearranging the terms to standard form:
[tex]\[ 3x^2 - 8x - 10 = 4 \\ 3x^2 - 8x - 10 - 4 = 0 \\ 3x^2 - 8x - 14 = 0 \][/tex]
This does not match the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex].
### Option C: [tex]\(3x^2 + 8x - 10 = -8\)[/tex]
Rearranging the terms to standard form:
[tex]\[ 3x^2 + 8x - 10 = -8 \\ 3x^2 + 8x - 10 + 8 = 0 \\ 3x^2 + 8x - 2 = 0 \][/tex]
This matches the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex].
### Option D: [tex]\(-2x^2 + 8x - 3 = 4\)[/tex]
Rearranging the terms to standard form:
[tex]\[ -2x^2 + 8x - 3 = 4 \\ -2x^2 + 8x - 3 - 4 = 0 \\ -2x^2 + 8x - 7 = 0 \][/tex]
This does not match the form [tex]\( 3x^2 + 8x - 2 = 0 \)[/tex].
Thus, the only equation that matches the given standard form is option:
[tex]\[ C: 3x^2 + 8x - 10 = -8 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.