Question

If the zeros of the polynomials x³ -2x² + x + 1 are (a -b), (a) and (a + b), then find the values of a and b.​

Answer 1

Answer:

a = 2/3

b = √(35/18)

Step-by-step explanation:

x³ - 2x² + x + 1 = 0

Let a = 1

b = -2

c = 1

d = 1

In a cubic equation, the sum of the roots = -b/a = -(-2)/1 = 2

=> a-b+a+a+b = 2

=> 3a = 2

=> a = 2/3

Now, product of roots = -d/a = -(1)/1 = -1

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

=> a(a²-b²) = -1

=> a³ - ab² = -1

Putting a = 2/3 here,

=> (2/3)³ - 2/3(b²) = -1

=> 8/27 - 2b²/3 = -1

=> 2b²/3 = 8/27 + 1 = 35/27

=> b² = 35/27 x 3/2 = 105/54 = 35/18

=> b = √(35/18)