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If and are the roots of 2 x x 5 3 0then the value of 1 1 a ?
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If and are the roots of 2 x x 5 3 0then the value of 1 1 a ...
**Solution:**
Given equation: 2x^2 + 5x + 3 = 0
To find the value of 1 + 1/αβ, we need to find the value of α and β first.
**Finding the Roots:**
The given equation is a quadratic equation in the form ax^2 + bx + c = 0, where a = 2, b = 5, and c = 3.
We can solve the quadratic equation to find the roots using the quadratic formula: x = (-b ± √(b^2 - 4ac))/2a.
Plugging in the values, we have:
α = (-5 + √(5^2 - 4*2*3))/(2*2) = (-5 + √(25 - 24))/4 = (-5 + √1)/4 = (-5 + 1)/4 = -4/4 = -1
β = (-5 - √(5^2 - 4*2*3))/(2*2) = (-5 - √(25 - 24))/4 = (-5 - √1)/4 = (-5 - 1)/4 = -6/4 = -3/2
**Calculating the Value:**
Now, we can calculate the value of 1 + 1/αβ.
1 + 1/αβ = 1 + 1/((-1)*(-3/2)) = 1 + 1/(3/2) = 1 + 2/3 = (3 + 2)/3 = 5/3
Therefore, the value of 1 + 1/αβ is 5/3.
**Conclusion:**
The value of 1 + 1/αβ is 5/3.
Given equation: 2x^2 + 5x + 3 = 0
To find the value of 1 + 1/αβ, we need to find the value of α and β first.
**Finding the Roots:**
The given equation is a quadratic equation in the form ax^2 + bx + c = 0, where a = 2, b = 5, and c = 3.
We can solve the quadratic equation to find the roots using the quadratic formula: x = (-b ± √(b^2 - 4ac))/2a.
Plugging in the values, we have:
α = (-5 + √(5^2 - 4*2*3))/(2*2) = (-5 + √(25 - 24))/4 = (-5 + √1)/4 = (-5 + 1)/4 = -4/4 = -1
β = (-5 - √(5^2 - 4*2*3))/(2*2) = (-5 - √(25 - 24))/4 = (-5 - √1)/4 = (-5 - 1)/4 = -6/4 = -3/2
**Calculating the Value:**
Now, we can calculate the value of 1 + 1/αβ.
1 + 1/αβ = 1 + 1/((-1)*(-3/2)) = 1 + 1/(3/2) = 1 + 2/3 = (3 + 2)/3 = 5/3
Therefore, the value of 1 + 1/αβ is 5/3.
**Conclusion:**
The value of 1 + 1/αβ is 5/3.
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If and are the roots of 2 x x 5 3 0then the value of 1 1 a ?
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If and are the roots of 2 x x 5 3 0then the value of 1 1 a ? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If and are the roots of 2 x x 5 3 0then the value of 1 1 a ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If and are the roots of 2 x x 5 3 0then the value of 1 1 a ?.
If and are the roots of 2 x x 5 3 0then the value of 1 1 a ? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If and are the roots of 2 x x 5 3 0then the value of 1 1 a ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If and are the roots of 2 x x 5 3 0then the value of 1 1 a ?.
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