Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the cofficients x²- 2x- 8​

Answer 1

Answer :-

Zeroes of the polynomial are -2 and +4

Step-by-step explanation :-

Given Quadratic equation → x² - 2x - 8

Factorise this equation by splitting the middle term.

x² - 2x - 8 = 0

⇒ x² + 2x - 4x - 8 = 0

⇒ x (x + 2) - 4 (x + 2) = 0

⇒ (x + 2) (x - 4) = 0

⇒ x = -2 or 4

So, the 2 roots of the equation are -2 and 4

Here, let's consider

• α as -2 and
• β as 4

Finding the sum of zeros:

Sum of zeros = -b/a

→ -2 + 4 = -(-2) ÷ 1

→ 2 = 2

Finding the product of zeros:

Product of zeros = c/a

→ 4 × (-2) = -8 ÷ 1

→ -8 = -8

★ HENCE VERIFIED ★