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If alpha and beta zeros of quadratic polynomial p of X equals to 6xsquare + X - 1 then find the value of Alpha / beta + beta / alpha + 2 into 1 upon alpha + 1 upon beta + 3 alpha beta?
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If alpha and beta zeros of quadratic polynomial p of X equals to 6xsqu...
- **Given Information**
Given quadratic polynomial p(x) = 6x^2 + x - 1 with zeros alpha and beta.
- **Finding the Value**
We are required to find the value of the expression:
\[ \frac{\alpha}{\beta} + \frac{\beta}{\alpha} + 2\left(\frac{1}{\alpha} + \frac{1}{\beta}\right) + 3\alpha\beta \]
- **Solution**
1. We know that the sum of zeros of a quadratic polynomial is given by:
\[ \alpha + \beta = -\frac{b}{a} \]
In this case, a = 6 and b = 1, so:
\[ \alpha + \beta = -\frac{1}{6} \]
2. Similarly, the product of zeros is given by:
\[ \alpha\beta = \frac{c}{a} \]
In this case, a = 6 and c = -1, so:
\[ \alpha\beta = -\frac{1}{6} \]
3. Substituting the values of alpha, beta, alpha + beta, and alpha*beta into the expression, we get:
\[ \frac{\alpha}{\beta} + \frac{\beta}{\alpha} + 2\left(\frac{1}{\alpha} + \frac{1}{\beta}\right) + 3\alpha\beta \]
\[ = \frac{-1/6}{-1/6} + \frac{-1/6}{-1/6} + 2\left(\frac{1}{-1/6} + \frac{1}{-1/6}\right) + 3*(-1/6) \]
\[ = 1 + 1 + 2*(-6) + (-1/2) \]
\[ = 2 - 12 - 1/2 \]
\[ = -10.5 \]
Therefore, the value of the expression is -10.5.
Given quadratic polynomial p(x) = 6x^2 + x - 1 with zeros alpha and beta.
- **Finding the Value**
We are required to find the value of the expression:
\[ \frac{\alpha}{\beta} + \frac{\beta}{\alpha} + 2\left(\frac{1}{\alpha} + \frac{1}{\beta}\right) + 3\alpha\beta \]
- **Solution**
1. We know that the sum of zeros of a quadratic polynomial is given by:
\[ \alpha + \beta = -\frac{b}{a} \]
In this case, a = 6 and b = 1, so:
\[ \alpha + \beta = -\frac{1}{6} \]
2. Similarly, the product of zeros is given by:
\[ \alpha\beta = \frac{c}{a} \]
In this case, a = 6 and c = -1, so:
\[ \alpha\beta = -\frac{1}{6} \]
3. Substituting the values of alpha, beta, alpha + beta, and alpha*beta into the expression, we get:
\[ \frac{\alpha}{\beta} + \frac{\beta}{\alpha} + 2\left(\frac{1}{\alpha} + \frac{1}{\beta}\right) + 3\alpha\beta \]
\[ = \frac{-1/6}{-1/6} + \frac{-1/6}{-1/6} + 2\left(\frac{1}{-1/6} + \frac{1}{-1/6}\right) + 3*(-1/6) \]
\[ = 1 + 1 + 2*(-6) + (-1/2) \]
\[ = 2 - 12 - 1/2 \]
\[ = -10.5 \]
Therefore, the value of the expression is -10.5.
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If alpha and beta zeros of quadratic polynomial p of X equals to 6xsquare + X - 1 then find the value of Alpha / beta + beta / alpha + 2 into 1 upon alpha + 1 upon beta + 3 alpha beta?
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If alpha and beta zeros of quadratic polynomial p of X equals to 6xsquare + X - 1 then find the value of Alpha / beta + beta / alpha + 2 into 1 upon alpha + 1 upon beta + 3 alpha beta? 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 alpha and beta zeros of quadratic polynomial p of X equals to 6xsquare + X - 1 then find the value of Alpha / beta + beta / alpha + 2 into 1 upon alpha + 1 upon beta + 3 alpha beta? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta zeros of quadratic polynomial p of X equals to 6xsquare + X - 1 then find the value of Alpha / beta + beta / alpha + 2 into 1 upon alpha + 1 upon beta + 3 alpha beta?.
If alpha and beta zeros of quadratic polynomial p of X equals to 6xsquare + X - 1 then find the value of Alpha / beta + beta / alpha + 2 into 1 upon alpha + 1 upon beta + 3 alpha beta? 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 alpha and beta zeros of quadratic polynomial p of X equals to 6xsquare + X - 1 then find the value of Alpha / beta + beta / alpha + 2 into 1 upon alpha + 1 upon beta + 3 alpha beta? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta zeros of quadratic polynomial p of X equals to 6xsquare + X - 1 then find the value of Alpha / beta + beta / alpha + 2 into 1 upon alpha + 1 upon beta + 3 alpha beta?.
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