1.

If Alpha and beta are the zeroes of x²-px+q, then find the value of alpha/ beta+beta/alpha.

Answer» HI...☺

Here is your answer...✌

Given that,

α and β are zero of x² - PX + q

We know that,

sum \: of \: zeros = \frac{ - b}{a} \\ \\ \alpha + \beta = \frac{ - ( - p)}{1} \\ \\ \alpha + \beta = p \: \:\: \: \: \: \: \:.....(1)\\
And

product \: of \: zeros = \frac{c}{a} \\ \\ \alpha \beta = \frac{q}{1} \\ \\ \alpha \beta = q \: \:\: \: \: \: \: \:.....(2)

Now

\frac{ \alpha }{ \beta} + \frac{ \beta }{ \alpha } = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } \\ \\ = \frac{ {( \alpha + \beta) }^{2} - 2 \alpha \beta }{ \alpha \beta } \\ \\ = \frac{ {p}^{2} - 2q}{q}\: \:\: \: \: \: \: \:[ from\: (1) \:and\: (2) ]


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