Question

If the zeroes of the polynomial 2x^3 - 15x^2 + 37x - 30 are a-b , a , a+b , Find all zeroes...

Answer 1

➵ p(x) = 2x³ - 15x² + 37x - 30

According to rules of polynomials

➵  a + (a - b) + (a + b) = - (- 15)/2

➵ 3a = 15/2

➵ a = 5/2

______________________________

➵ a(a-b)+(a-b)(a+b)+(a+b)a=37/2

➵ a² - ab + a² - b² + a² + ab=37/2

➵ 3a² - b² = 37/2

➵ 3(5/2)² - 37/2 = b²

➵ 75/4 - 74/4 = b²

➵ b = +/- 1/2

______________________________

So one of the zero is 5/2

Another zeros are :

Case 1 : If b = + 1/2

Then a + b = 5/2 + 1/2

= 3

and a - b = 5/2 - 1/2

= 2

Case 2 : If b is - 1/2

Then a + b = 5/2 - 1/2

= 2

and a - b = 5/2 + 1/2

= 3