Find the zeroes of the quadratic polynomial 2x² – 8x + 6 and examine the truth of the relationship between the zeroes and the coefficients.

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

2x² – 8x + 6 = 0

To factorize the polynomial we have,

Sum of the value should be equal = -8

Product should be equal to = 2 × 6

= 12

So two numbers are -2, -6

2x² – 2x – 6x + 6 = 0

2x(x – 1) – 6(x – 1) = 0

(2x-6)(x – 1) = 0

2x-6 = 0 or x-1 = 0

Solving first part,

2x-6 = 0

2x = 6

x = 3

Solving 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 = 2, b = -8, c = 6

Sum of zeroes = -b / a

= - (-8) / 2

= 4

Product of zeroes = c / a

= 6 / 2

= 3

Zeroes obtained are 3 and 1 and their sum is 4 and product is 3 which is matching to the answer obtained through the ratio of coefficients.