Question

find the zeros of the quadratic polynomial 2 x ^2 - 8 x + 6 and verify the relation between zeros and its coefficient

Answer 1

Step-by-step explanation:

here is your answer and once try to solve it yourself

Answer 2

Given polynomial is 2x² - 8x + 6.

We have to find the zeros of the above polynomial.

The above equation is in the form ax² + bx + c = 0.

We have to split the middle term in such a way that their sum is b (-8x) and the product is ac (2*6x² = 12x²)

→ 2x² - 8x + 6 = 0

By Splitting the middle term, we get

→ 2x² - 6x - 2x + 6 = 0

→ 2x(x - 3) -2(x - 3) = 0

→ (2x - 2) (x - 3) = 0

On comparing we get,

→ x = 2/2, 3

→ x = 1, 3

Therefore, zeros are 1 and 3.

Now in given polynomial; a = 2, b = -8 and c = 6

Verification

Sum of zeros = -b/a

1 + 3 = -(-8)/2

4 = 4

Product of zeros = c/a

1 × 3 = 6/2

3 = 3