Question

if 1 is a zero of the polynomial p (x) =ax²-3 (a-1)x -1 .then the value of a.​

Answer 1

Answer:

$\huge\boxed{a=1}$

Step-by-step explanation:

$\text{If 1 if a zero of the polynomial}\ p(x)=ax^2-3(a-1)x-1,\ \text{then}\ p(1)=0.$

$\text{Substitute:}\\\\a(1^2)-3(a-1)(1)-1=0\\\\a-3(a-1)-1=0\\\\a-3a+3-1=0\qquad|\text{combine like terms}\\\\(a-3a)+(3-1)=0\\\\-2a+2=0\qquad|\text{subtract 2 from both sides}\\\\-2a=-2\qquad|\text{divide both sides by (-2)}\\\\a=1$