Question

If alpha and beta is zeros of polynomial x²-4√3x+3, then find the value of alpha + beta -alpha beta ​

Answer 1

Hello mate !!!

Here is your answer :

p(x) = x² - 4√3x + 3

First, we have to find the sum and products of it's roots...

It is quadratic equation so it has two roots...

$Let \: its \: roots \: be \: \alpha (alpha) \: and \: \beta (beta)$

Here, a = 1 ( coefficient of x² )

b = -4√3 ( coefficient of x )

c = 3 ( constant term )

SUM OF ROOTS ⤵

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

$\\ \alpha + \beta = \frac{ - ( - 4 \sqrt{3} )}{1}$

$\\ \alpha + \beta = 4 \sqrt{3}$

PRODUCTS OF ROOTS ⤵

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

$\\ \alpha \beta = \frac{3}{1}$

$\alpha \beta = 3$

We have to find the value of

$= > \alpha + \beta - \alpha \beta$

Putting the values from above...

$= > 4 \sqrt{3} - 3$

Hope it helps u ..

Answer 2

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

$\bf{GIVEN \colon - }$

p(x) = x² - 4√3x + 3

.

→ Here as it is a quadratic polynomial

hence

» it is in the form

→ ax² + bx + c

Hence ,

» a = 1 , b = 4√3 , c = 3

$\begin{lgathered}\\ \bf{\alpha + \beta = \frac{ - b}{a}}\end{lgathered}$

$\begin{lgathered}\\ \bf{\alpha + \beta = \frac{ - ( - 4 \sqrt{3} )}{1}}\end{lgathered}$

$\begin{lgathered}\\ \bf{\alpha + \beta = 4 \sqrt{3}}\end{lgathered}$

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

$\bf{\alpha\times\beta=\frac{3}{1}}$

$\bf{\alpha \beta =3}}$

Now ,

we will find the value of

→ α + β− αβ

$\huge \bf \pink{ \implies 4 \sqrt{3} - 3}$