Question

If alpha and beta are zeros of polynomial f x is equal to x square - 5 x + K said that Alpha minus beta is equal to 1 find the value of k

Answer 1

the answer is below:
$\alpha - \beta = 1 \: \: \: \: \: \: \: \: \: \: \: (i)\\ \beta = \alpha - 1 \\ x { }^{2} - 5 + k \\ \alpha + \beta = \frac{ - c}{a} \\ \alpha + \beta = \frac{5}{1} \: \: \: \: \: \: \: \: (ii) \\ adding \: eq ^{n} (i )\: and \: (ii) \\ 2 \alpha = 6 \\ \alpha = 3 \\ \beta = 2 \\ now \: \\ product \: of \: zeroes = \frac{c}{a} \\ \alpha \beta = \frac{k}{1 } \\ 3 \times 2 = k \\ k = 6$
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