Question

if the zero of polynomial x square minus 3 X square + X + 1 are (a +b), a, (a+b) find the value of a and b​

Answer 1

Answer:

a = 1 & b = ± √2

Step-by-step explanation:

if the zero of polynomial x³ - 3x² + x + 1 are (a - b), a, (a+b) find the value of a and b​

Sum of roots = - (-3)/1 = 3  =  a - b + a + a + b  = 3a

=> a = 1

a(a-b) + a(a+b) + (a -b)(a+b) = 1/1

=> a² - ab  + a² + ab + a² - b² = 1

=> 3a² - b² = 1

=> 3(1)² - b² = 1

=> b² = 2

=> b = ± √2

Another way

( x - (a -b))(x - a) (x - ( a + b)

= (x-a)(x - ( a + b) )( x - (a -b))

=  (x-a)(x² - x(a - b + a + b) + (a² - b²) )

=  (x-a)(x² - 2ax + (a² - b²) )

= x³ - 2ax² + (a² - b²)x  -ax² +2a²x - a (a² - b²)

= x³ - 3ax² + (3a² - b²)x - a (a² - b²)

Equating with

x³ - 3x² + x + 1

-3a = -3

=> a = 1

3a² - b² = 1

=> 3  - b² = 1

=> b = ± √2