Question

if alpha and beta are the zeros of the quadratic polynomial 6x2 + x - 2 find the value of Alpha upon beta + beta upon Alpha

Answer 1

here is answer to this question

Answer 2

Answer:

The value of $\bold{\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=-2 \frac{1}{12}}$

Solution:

$6 x^{2}+x-2$

Factorizing the above equation we get,

$6 x^{2}+4-3 x-2$

= (3x + 2) (2x – 1)

3x + 2 = 0, x = (-2)/3

2x – 1 = 0, x = 1/2

The two values of x are taken as α and β respectively.

$\alpha=\frac{-2}{3}, \quad \beta=\frac{1}{2}$

To find $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$

$\begin{array}{l}{\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\frac{-2}{3}}{\frac{1}{2}}+\frac{\frac{1}{2}}{\frac{-2}{3}}} \\ {=\frac{-2}{3} * \frac{2}{1}+\frac{1}{2} * \frac{3}{-2}} \\ {=\frac{-16}{3}+\frac{-3}{4}} \\ {=\frac{-16}{12}-\frac{9}{12}}\end{array}$

Therefore the values of $\bold{\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=-2 \frac{1}{12}}$