Find the zeroes o

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.