Question

Find the zeroes of the polynomial x +1/6x-2 and verify the relationship between the coefficients and zeroes of the polynomial.​

Answer 1

Answer:

Given: The polynomial x^2 + 1/6(x) - 2

To find:  The zeroes of the polynomial and verify the relation between the coefficient and zeroes of the polynomial.

Solution:

Now we have given the polynomial: x^2 + 1/6(x) - 2 = 0

Simplifying it, we get:

              6x^2 + x - 12 = 0

So by splitting middle term, we get:

              6x^2 - 8x + 9x - 12 = 0

Now combining the terms, we get:

              (6x^2 - 8x) + (9x - 12) = 0

              2x(3x - 4) + 3(3x + 4) = 0

              (3x - 4)(2x + 3) = 0

              x = 4/3 or x = -3/2

So verifying it, we get:

Sum of zeroes: 4/3 - 3/2 = -1/6

Product of zeroes: 4/3 x (-3/2) = -2

Hence verified.

Answer:

               So the zeroes of the polynomial are 4/3 and -3/2.