Question

If zeros of a polynomial x 3 -3x 2 +x+1 are a-b, a and a+b find a and b

Answer 1

sum of zeros = -b/a
(a-b)+a+(a+b)=-b/a
3a+b-b=3
3a=3
a=1

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Here we have

★Zeroes of Polynomial are (a - b) , a , (a + b)

★Hence :-

★Sum of zeroes of polynomial :-

${\boxed{\sf\:{\dfrac{-b}{a}}}}$

$\tt{\rightarrow (a-b),a,(a+b)=\dfrac{-(-3)}{1}=3}$

3a = 3

$\tt{\rightarrow a=\dfrac{3}{3}}$

a = 1

★Now :-

$\tt{\rightarrow (a-b)a+a(a+b)+(a+b)(a-b) =\dfrac{1}{1}=1}$

a² - ab + a² + ab + a² - b² = 1

3a² - b² = 1

★Here substitute the value of a we get :-

3(1)² - b² = 1

3 - b² = 1

b² = 2

b = ± √2

★Hence we get :-

a = 1 and b = ±√2