Question

If the zeroes of the polynomial x3 – 3x2 + x + 1 are a–b, a, a+b, find a and b.

Answer 1

SOLUTION
Since, (a - b), a, (a + b) are the zeroes of the polynomial x3 – 3x2 + x + 1. Therefore, sum of the zeroes = (a - b) + a + (a + b) = -(-3)/1 = 3
⇒ 3a = 3 ⇒ a =1∴ Sum of the products of is zeroes taken two at a time = a(a - b) + a(a + b) + (a + b) (a - b) =1/1 = 1 a2 - ab + a2 + ab + a2 - b2 = 1 ⇒ 3a2 - b2 =1Putting the value of a,⇒ 3(1)2 - b2 = 1 ⇒ 3 - b2 = 1 ⇒ b2 = 2 ⇒ b = ±√2 Hence, a = 1 and b = ±√2

Answer 2

Vant Hoff factor predicts the nature of solute in solution.