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

3x² – x – 4

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

3x² – x - 4 = 0

To factorize the polynomial we have,

Sum of the value should be equal = -1

Product should be equal to = 3 × (-4)

= -12

So two numbers are -4, 3

3x² – 4x + 3x - 4 = 0

3x (x + 1) -4 (x + 1) = 0

(3x - 4)(x + 1) = 0

3x - 4 = 0 or x + 1 = 0

Now solving first part,

3x-4 = 0

3x = 4

x = 4/3

Now solving the second part,

x + 1 = 0

x = -1

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

ax² + bx + c = 0

∴ a = 3, b = -1, c = -4

Sum of zeroes = -b / a

= - (-1) / 3

= 1/3

Product of zeroes = c / a

= -4 / 3

= -4/3