Question

If alpha and beta are the zero and the quadratic polynomial p(x)=x^2-x-4, then the value of 1/alpha^2+1/beta^2-alphabeta is

Answer 1

Answer:

$x^2 - x - 4 =0$

To find:

$\frac{1}{\alpha^2 } + \frac{1}{\beta^2 } - \alpha \beta$

$\frac{\alpha^2 + \beta^2 }{\alpha^2\beta^2} - \alpha \beta$

$\frac{(\alpha + \beta )^2 - 2\alpha \beta}{(\alpha \beta)^2}$ $-\alpha \beta$

From The quadratic equation we have

$\alpha +\beta = 1\\\\\alpha \beta = -4$

1 -2.(-4)/(-4)^2 - (-4)

1+8/16+4

9/16+ 4 = 73/4

Sorry my mistake