Class 10 Exam > Class 10 Questions > If π πππ π are the roots of the quadrati...
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If π πππ π are the roots of the quadratic equation π₯
2 + ππ₯ β π = 0, then findπ πππ π.?
2 + ππ₯ β π = 0, then findπ πππ π.?
Most Upvoted Answer
If π πππ π are the roots of the quadratic equation π₯ 2 + ππ₯ β ...
Solution:
Given Quadratic Equation:
The given quadratic equation is: $x^2 + ax - b = 0$.
Roots of the Quadratic Equation:
Let the roots of the quadratic equation be $x = a$ and $x = b$.
Sum and Product of Roots:
The sum of the roots of a quadratic equation is given by the formula: $a + b = -\frac{b}{a}$.
The product of the roots of a quadratic equation is given by the formula: $ab = \frac{-b}{a}$.
Comparing with the Given Quadratic Equation:
From the given quadratic equation, we can see that the sum of the roots ($a + b$) is equal to $-a$ and the product of the roots ($ab$) is equal to $-b$.
Therefore, the values of a and b are:
- $a = -a$
- $b = -b$
Conclusion:
The values of $a$ and $b$ are equal to the negative of the coefficients of $x$ and the constant term in the given quadratic equation, respectively.
Given Quadratic Equation:
The given quadratic equation is: $x^2 + ax - b = 0$.
Roots of the Quadratic Equation:
Let the roots of the quadratic equation be $x = a$ and $x = b$.
Sum and Product of Roots:
The sum of the roots of a quadratic equation is given by the formula: $a + b = -\frac{b}{a}$.
The product of the roots of a quadratic equation is given by the formula: $ab = \frac{-b}{a}$.
Comparing with the Given Quadratic Equation:
From the given quadratic equation, we can see that the sum of the roots ($a + b$) is equal to $-a$ and the product of the roots ($ab$) is equal to $-b$.
Therefore, the values of a and b are:
- $a = -a$
- $b = -b$
Conclusion:
The values of $a$ and $b$ are equal to the negative of the coefficients of $x$ and the constant term in the given quadratic equation, respectively.
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If π πππ π are the roots of the quadratic equation π₯ 2 + ππ₯ β π = 0, then findπ πππ π.?
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If π πππ π are the roots of the quadratic equation π₯ 2 + ππ₯ β π = 0, then findπ πππ π.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If π πππ π are the roots of the quadratic equation π₯ 2 + ππ₯ β π = 0, then findπ πππ π.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If π πππ π are the roots of the quadratic equation π₯ 2 + ππ₯ β π = 0, then findπ πππ π.?.
If π πππ π are the roots of the quadratic equation π₯ 2 + ππ₯ β π = 0, then findπ πππ π.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If π πππ π are the roots of the quadratic equation π₯ 2 + ππ₯ β π = 0, then findπ πππ π.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If π πππ π are the roots of the quadratic equation π₯ 2 + ππ₯ β π = 0, then findπ πππ π.?.
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