Question

find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient
$x {2} - 2x - 8$
​

Answer 1

EXPLANATION.

Quadratic polynomial.

⇒ x² - 2x - 8.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ x² - 4x + 2x - 8 = 0.

⇒ x(x - 4) + 2(x - 4) = 0.

⇒ (x + 2)(x - 4) = 0.

⇒ x = - 2   and   x = 4.

⇒ Sum = - 2 + 4 = 2.

⇒ Products = (-2) x 4 = - 8.

Quadratic polynomial.

⇒ x² - 2x - 8.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

⇒ α + β = -(-2)/1 = 2.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ αβ = - 8.

Hence proved.

Answer 2

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