Question

If 1 is a zero of the polynomial $p(x) =ax^{2}-3(a-1)x-1,$, then find the value of a.

Answer 1

SOLUTION :  

Given : p(x) = ax² - 3(a - 1)x -1  

Since, x = 1 is a zero of polynomial p(x).

Therefore, p(1) = 0

p(x) = ax² - 3(a - 1)x -1  

p(x) = ax² - 3ax + 3x -1  

a(1)² - 3a(1) + 3(1) - 1 = 0

a - 3a + 3 -1 = 0

-2a + 2 = 0

-2a = -2  

2a = 2  

a = 2/2  

a = 1

Hence, the value of a is 1.

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Solution :-

Given,

$p(x) = {a}^{2} - 3(a - 1)x - 1$
x=1 is a zero of the polynomial

Let put the vale of x in the given polynomial
$p(x) = {ax}^{2} - 3(a - 1)x - 1 \\ \\ a {(1)}^{2} - 3(a - 1)1 - 1 = 0 \\ \\ a - 3a + 3 - 1 = 0 \\ \\ - 2a + 2 = 0 \\ \\ 2 = 2a \\ \\ \frac{2}{2} = a \\ \\ a = 1 \: ans$
==============
@GauravSaxena01