Question

find the zeroes of the polynomial x^2+1/6x-2 and verify the realtion between the coefficient and zeroes of the polynomial.

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation: x^2+1/6x+2=0

by simplifying the equation we get 6x^2+x-12=0

if we factories the equation, then we get zeros as

-3/2 and 4/3