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4-2.Quadratic Equations and Inequations
easy
यदि $\alpha , \beta , \gamma $ समीकरण ${x^3} + a{x^2} + bx + c = 0$ के मूल हों, तो ${\alpha ^{ - 1}} + {\beta ^{ - 1}} + {\gamma ^{ - 1}} = $
A
$a/c$
B
$-b/c$
C
$b/a$
D
$c/a$
Solution
$\alpha , \beta , \gamma $ समीकरण
${x^3} + a{x^2} + bx + c = 0$ के मूल हैं
$\therefore $ $\alpha + \beta + \gamma = – a$, $\alpha \beta + \beta \gamma + \gamma \alpha = b$ और $\alpha \beta \gamma = – \,c$
${\alpha ^{ – 1}} + {\beta ^{ – 1}} + {\gamma ^{ – 1}}$ $ = \frac{1}{\alpha } + \frac{1}{\beta } + \frac{1}{\gamma }$ $ = \frac{{\alpha \beta + \beta \gamma + \gamma \alpha }}{{\alpha \beta \gamma }}$
$ = – b/c$.
Standard 11
Mathematics
