Question

If alpha , beta are the zeros of the polynomial f(x) = ax^2 +bx + c , then find 1/alpha^2 +1/beta^2

Answer 1

Answer:

Step-by-step explanation:

Let α , β be the root of given polynomial.

Then

$\alpha +\beta =\frac{-b}{a}$

$\alpha \beta =\frac{c}{a}$

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

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

                                                      $=\frac{(\frac{-b}{a})^2-2(\frac{c}{a})}{(\frac{c}{a})^2}\\=\frac{(\frac{b^2}{a^2})-\frac{2c}{a}}{\frac{c^2}{a^2}} \\=\frac{ab^2-2a^2c}{a^3}X\frac{a^2}{c^2}\\=\frac{a(b^2-2ac)}{a}X\frac{1}{c^2}\\=\frac{b^2-2ac}{c^2}$

Answer 2

Answer:

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