Question

If the zeroes of the polynomial x^3-3x^2+x + 1 are a - b, a, a + b find a and b​

Answer 1

Solution :-

Given Root of the equation

x³ - 3x² + x + 1 = 0

are

a - b , a , a + b

Now as we know that

Sum of roots

= α+β+γ

= -B/A

Product of roots taken two at a time

= αβ + βγ + αγ

= C/A

Product of roots

= αβγ

= -D/A

Now as in our polynomial

A = 1

B = -3

C = 1

D = 1

Now we will use it for our calculations :-

Sum of roots

→ (a - b) + a + (a + b) = -(-3)/1

→ 3a = 3

→ a = 1

Now product of roots

→ (a - b)(a)(a + b) = -(1)/1

→(1 - b)(1)( 1 + b) = -1

→ 1² - b² = -1

→ b² = 2

→ b = ±√2

So

a = 1

b = ±√2