Question

find the zeros of the quadratic polynomial 5 x square - 4 - 8X and verify the relationship between the zeros and the coefficient of the given polynomial​

Answer 1

Answer:

Given polynomial

5x²-8x-4

5x²-10x+2x-4

5x(x-2)+2(x-2)

(x-2)(5x+2)

The zeroes of given polynomial are

2,-2/5

We ca verify by substituting them in the polynomial.

Answer 2

$5 {x}^{2} - 8x - 4 = 0\\ 5 {x}^{2} - 10x + 2x - 4 = 0\\ 5x(x - 2) + 2(x - 2) = 0 \\ (x - 2)(5x + 2) = 0 \\ x = 2 \: or \: x = \dfrac{ - 2}{5} \\ \\ so \: \alpha = 2 \: and \: \beta = \dfrac{ - 2}{5} \\ \\ \alpha + \beta = 2 - \frac{2}{5} = \frac{8}{5} = \frac{ - b}{a} \\ \\ \alpha \beta = 2 \times( \frac{ - 2}{5} ) = \frac{ - 4}{5} = \frac{c}{a}$_______________

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