Question

if alpha and beta are zeros of quadratic polynomial f(x)=3^2--6x+4.
Find alpha /beta +2{alpha+beta /alpha beta}+3alpha beta

Answer 1

Dear student
$$\begin{gathered} \mathrm{Since}\mathrm{\alpha }\mathrm{and}\mathrm{\beta }\mathrm{are}\mathrm{the}\mathrm{zeros}\mathrm{of}\mathrm{the}\mathrm{polynomial}. \\ \mathrm{Therefore},\mathrm{\alpha }+\mathrm{\beta }=\frac{6}{3}=2\mathrm{and}\mathrm{\alpha \beta }=\frac{4}{3} \\ \mathrm{So},\frac{\mathrm{\alpha }}{\mathrm{\beta }}+2\left[\frac{\mathrm{\alpha }+\mathrm{\beta }}{\mathrm{\alpha \beta }}\right]+3\mathrm{\alpha \beta } \\ =\frac{\mathrm{\alpha }}{\mathrm{\beta }}+2\left(\frac{2}{{\displaystyle \frac{4}{3}}}\right)+3\left(\frac{4}{3}\right) \\ =\frac{\mathrm{\alpha }}{\mathrm{\beta }}+2\left(2\times \frac{3}{4}\right)+4 \\ =\frac{\mathrm{\alpha }}{\mathrm{\beta }}+3+4 \\ =\frac{\mathrm{\alpha }}{\mathrm{\beta }}+7 \end{gathered}$$
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