Question

if x+1 is a factor of x^2-3ax+3x-7 then the value of a is​

Answer 1

Step-by-step explanation:

I hope it is correct answer

Answer 2

${ \colorbox{yellow}{\tt Question}}$

If x+1 is a factor of x² - 3ax + 3x -7 , then the value of a is

$\colorbox{blue}{\tt Answer}$

$\blue{\boxed{a = 3}}$

☯︎ Solution

This concept is basically based on Factor and Reminder Theorem. Now , Let's assume x - a is a factor of the a polynomial say f(x) this means that when the value of x is taken as a the polynomial would bear the remainder 0 i.e, f(a)=0

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Procedure

Given that ,

$\red{ \tt f(x) = {x}^{2} - 3ax + 3x - 7}$

Now , x + 1 = 0 ; x = - 1

Substitute the value of x in the given polynomial.

$\tt f( - 1) = ( - 1) ^{2} - 3a( - 1) + 3( - 1) - 7 = 0$

$\tt : \implies1 + 3a - 3 - 7 = 0 \\ \tt : \implies 3a - 10 + 1 = 0 \\ \tt : \implies 3a - 9 = 0 \\ : \implies \tt 3a = 9 \\ \leadsto \tt a = \cancel \frac{9}{3} = \colorbox{cyan} 3$

$\begin{gathered} \\ {\blue{\underline{\rule{75pt}{9pt}}}}{\color{maroon}{\underline{\rule{75pt}{9pt}}}}{\color{cyan} {\underline{\rule{75pt}{9pt}}}}\end{gathered}$

Thankyou