Question

if the zeros of polynomial x^3-3x^2+x+1 are a-b,a,a+b.find a and b

Answer 1

heya!!

refer to given attachment please

Remember some rules :-

for a cubic polynomial ax³ + bx² + cx + d

sum of zeros = -(b/a)

sum of product of zeroes taken two at a time = ( c/a)

product of zeros = (d/a)

Answer 2

Heya,

♦ Polynomial → p( x ) = x³ - 3x² + x + 1

You know =_= there's a hell long process but right now, I'll advise this :

→ p( 1 ) = ( 1 )³ - 3( 1 )² + 1 + 1 
              = 3 - 3 = 0

=> p( x ) = ( x - 1 )( x² - 2x - 1 )

Now, roots of g( x ) = ( x² - 2x - 1 ) :

→ Roots are : ( 1 + √2 ) , ( 1 - √2 )  [ by Quadratic Formula ]

=> Roots of p( x ) are : ( 1 - √2 ) , 1 , ( 1 + √2 )

=> Comparing, a = 1 ; b = ± √2