Q4 of 44 Page 67

Verify that 1, -1 and -3 are the zeroes of the cubic polynomial x3 + 3x2 – x - 3 and check the relationship between zeroes and the coefficients.

P(x) = x3 + 3x2 – x – 3

For x = 1,


⇒ P(1) = 13 + 3(1)2 – 1 – 3


⇒ P(1) = 1+ 3 – 1 – 3


⇒ P(1) = 0


For x = -1,


⇒ P(-1) = (-1)3 + 3(-1)2 – (-1) – 3


⇒ P(-1) = -1+ 3 + 1 – 3


⇒ P(-1) = 0


For x = -3,


⇒ P(-3) = (-3)3 + 3(-3)2 – (-3) – 3


⇒ P(-3) = -27+ 27 + 3 – 3


⇒ P(-3) = 0


Now,



Sum of zeroes = 1 + (-1) + (-3) = -3


Hence,



And,



Product of zeroes = 1 × (-1) × (-3) = -3



More from this chapter

All 44 →
3

Find the quadratic polynomial, for the zeroes given in each case.

1/4, -1

 3

Find the quadratic polynomial, for the zeroes given in each case.

1/2, 3/2

 1

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 - 2

 1

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 - x