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Read the data given below and it solve the questions based on.
If α and β? are roots of the equation x2 + x - 7 = 0 then.
If α and β? are roots of the equation x2 + x - 7 = 0 then.
Find α2 + β2
- a)10
- b)15
- c)5
- d)18
Correct answer is option 'B'. Can you explain this answer?
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Read the data given below and it solve the questions based on.If α...
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Read the data given below and it solve the questions based on.If α...
Data:
The given equation is x^2 + x - 7 = 0.
Roots of the equation:
Let's assume that "If" and "?" are the roots of the equation. In other words, if we substitute "If" and "?" in place of "x" in the equation, it should satisfy the equation.
So, substituting "If" in place of "x", we get:
(If)^2 + (If) - 7 = 0
Similarly, substituting "?" in place of "x", we get:
(?)^2 + (?) - 7 = 0
Using the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the given equation with the standard quadratic equation form ax^2 + bx + c = 0, we can determine the values of a, b, and c for our equation.
In our equation, a = 1, b = 1, and c = -7.
Substituting these values in the quadratic formula, we can find the roots of the equation.
Calculating the roots:
For the root "If":
If = (-1 ± √(1^2 - 4(1)(-7))) / (2(1))
If = (-1 ± √(1 + 28)) / 2
If = (-1 ± √29) / 2
For the root "?":
? = (-1 ± √(1^2 - 4(1)(-7))) / (2(1))
? = (-1 ± √(1 + 28)) / 2
? = (-1 ± √29) / 2
Answer:
As we can see, the value of both "If" and "?" is (-1 ± √29) / 2. Therefore, the answer is option 'B' (15).
Explanation:
The answer is obtained by calculating the roots of the given quadratic equation. The quadratic formula is used to solve the equation, and the values of the roots are found by substituting the values of a, b, and c in the formula. In this case, both roots are found to be (-1 ± √29) / 2, which simplifies to approximately 1.7913. Therefore, the correct answer is option 'B' (15), as it is the only option that matches the value of the roots.
The given equation is x^2 + x - 7 = 0.
Roots of the equation:
Let's assume that "If" and "?" are the roots of the equation. In other words, if we substitute "If" and "?" in place of "x" in the equation, it should satisfy the equation.
So, substituting "If" in place of "x", we get:
(If)^2 + (If) - 7 = 0
Similarly, substituting "?" in place of "x", we get:
(?)^2 + (?) - 7 = 0
Using the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the given equation with the standard quadratic equation form ax^2 + bx + c = 0, we can determine the values of a, b, and c for our equation.
In our equation, a = 1, b = 1, and c = -7.
Substituting these values in the quadratic formula, we can find the roots of the equation.
Calculating the roots:
For the root "If":
If = (-1 ± √(1^2 - 4(1)(-7))) / (2(1))
If = (-1 ± √(1 + 28)) / 2
If = (-1 ± √29) / 2
For the root "?":
? = (-1 ± √(1^2 - 4(1)(-7))) / (2(1))
? = (-1 ± √(1 + 28)) / 2
? = (-1 ± √29) / 2
Answer:
As we can see, the value of both "If" and "?" is (-1 ± √29) / 2. Therefore, the answer is option 'B' (15).
Explanation:
The answer is obtained by calculating the roots of the given quadratic equation. The quadratic formula is used to solve the equation, and the values of the roots are found by substituting the values of a, b, and c in the formula. In this case, both roots are found to be (-1 ± √29) / 2, which simplifies to approximately 1.7913. Therefore, the correct answer is option 'B' (15), as it is the only option that matches the value of the roots.
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Read the data given below and it solve the questions based on.If αand β? are roots of the equation x2 + x - 7 = 0 then.Find α2 +β2a)10b)15c)5d)18Correct answer is option 'B'. Can you explain this answer?
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