Question

if alpha and beta are the roots of the equation ax2+bx+c=0 the one of the quadratic equations are 1/alpha and 1/beta is​

Answer 1

$\huge\underline\mathrm{GivEn:-}$

⭐ It is given that $\alpha$ and $\beta$ are the zeroes of quadratic polynomial ax² + bx + c

$\huge\underline\mathrm{To\: find:-}$

⭐ The value of $\large{\sf {\frac{1}{alpha}}}$ + $\large{\sf {\frac{1}{beta}}}$

$\huge\underline\mathrm{SoLutioN:-}$

We know that,

• $\alpha + \beta = \frac{ - b}{a}$

and,

• $\alpha \times \beta = \frac{c}{a}$

According to Question :-

$\implies$$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta }$

We know the value of $\alpha$ + $\beta$ & $\alpha$$\beta$

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

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

$\implies$$\frac{ \alpha + \beta }{ \alpha \beta } = \large{\sf {\frac{-b}{c}}}$

$\huge\underline\mathrm{ThAnKs...}$

Answer 2

Answer:

$\alpha \: + \beta \div \alpha \beta = - b \div c$

$\large\underline\mathrm{Given:-}$

• if alpha and beta are the roots of the equation ax2+bx+c=0

$\large\underline\mathrm{To \: find}$

$The \: value \: of \: 1 \div \alpha + 1 \div \beta$

$\large\underline\mathrm{Solution}$

We know that,

$\alpha + \beta = - b \div a$

and

$\alpha \beta = c \div a$

$The \: value \: of \: \alpha + \beta \: and \: \: \alpha \beta .$

$\alpha + \beta \div \alpha \beta = (- b \div a) \div (c \div a)$

$\alpha + \beta \div \alpha \beta = - b \div c$