Question

If a - b , a and a + b are zeroes of the polynomial x ^ 3 - 15x ^ 2 + 71x - 105 Then find a and b.​

Answer 1

Answer:

Step-by-step explanation:

As the zeroes are in AP, let the zeroes be a-d, a, a+d.

The sum of zeroes of the given polynomial is -(-15)/1 = 15.

Therefore, a-d + a + a+d=15. Hence, a = 5.

Also, the product of zeroes is -(-105)/1 = 105.

Therefore, 5(5-d)(5+d)=105, or 25 - d^2 = 21.

Then, d^2 = 4. Hence, d=+-2.

Therefore, the zeroes are 3, 5, 7.