Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

6x² – x – 2

To find the zeros of the polynomial let us first solve the polynomial by equating it to zero. Factorizing the given polynomial

6x² – x - 2 = 0

To factorize the polynomial we have,

Sum of the value should be equal = -1

Product should be equal to = 6 × (-2)

= -12

So two numbers are -4, 3

6x² – 4x + 3x - 2 = 0

2x (3x – 2) + 1(3x – 2) = 0

(2x+1)(3x-2) = 0

2x+1 = 0 or 3x-2 = 0

Now Solving first part,

2x+1 = 0

2x = -1

x = -1/2

Now solving the second part,

3x-2 = 0

3x = 2

x = 2/3

When we compare the above quadratic equation with the generalized one we get,

ax² + bx + c = 0

∴ a = 6, b = -1, c = -2

Sum of zeroes = -b / a

= - (-1) / 6

= 1/6

Product of zeroes = c / a

= -2 / 6

= -1/3