Question

if alpha and beta are zeroes of 4x2 3x 7 then find the value of 1/alpha+1/beta -alpha beta please answer​

Answer 1

$\large \dag$ Appropriate Question :-

If $\large \alpha$ and $\large \beta$ are zeroes of 4x² + 3x × 7 then find the value of $\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta$

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{The   \: Value \:  of  \:given \:Expression \: is\: \frac{-61}{\:\:28} }} }$

$\large \dag$ Step by step Explanation :-

Here we have,

$\rm\text{Sum of Zeros } = \frac{ - b}{ \: \: a}$

$\large:\longmapsto \pmb{ \red{\rm \alpha + \beta = \frac{ - 3}{ \: \: 4} }}$

Also,

$\rm \text{Product of Zeros } = \frac{c}{a}$

$\large:\longmapsto \rm \red{ \pmb{ \alpha \beta = \frac{7}{4} }}$

Now,

$\: \: \: \: \: \: \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta$

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

❒ Putting Values from above ,

$= \dfrac{{ - 3}/{ \cancel 4} }{ {7}/{ \cancel4} } - \frac{7}{4}$

$= \frac{ - 3}{ \: \: 7} - \frac{7}{4}$

$= \frac{ - 12 - 49}{28}$

$= \frac{ - 61}{ \: \: 28}$

Therefore,

$\underline{\pink{\underline{\frak{\pmb{ \frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta = \frac{ - 61}{ \: \: 28} }}}}}$

Answer 2

Correct Question ⇝

If $\large \alpha$ and $\large \beta$ are zeroes of 4x² + 3x × 7 then find the value of $\frac{1}{ \alpha } + \frac{1}{ \beta } - \alpha \beta$

Solution ⇝

Here,

by formula of sum of zeros of a quadratic polynomial

$\large\pmb{ \red{ \boxed{ \underline{ \overline{ \alpha + \beta = \frac{ - 3}{4} }}}}}$

And also by formula of product of roots of a quadratic polynomial

$\large\pmb{ \blue{ \boxed{ \underline{ \overline{ \alpha \beta = \frac{ 7}{4} }}}}}$

now we have to calculate

$\red{= \frac{ \alpha + \beta }{ \alpha \beta } - \alpha \beta}$

$\frak{ = \dfrac{{ - 3}/{ 4} }{ {7}/{ 4} } - \frac{7}{4} }$

$\frak{ = \frac{ - 3}{ \: \: 7} - \frac{7}{4} }$

$\frak{ = \frac{ - 12 - 49}{28} }$

$\frak{ = \frac{ - 61}{ \: \: 28} }$

which is your Answer