Question

The roots α and β of the quadratic equation x2

-5x+3(k-1)=0 are such that αβ=1. Find the value k.​

Answer 1

${x}^{2} - 5x + 3(k - 1) = 0 \\ a = 1 \\ b = - 5 \\ c = 3(k - 1) \\ \\ \alpha \beta = 1 \\ \alpha \beta = \frac{c}{a} \\ \alpha \beta = 1 = \frac{c}{a} \\ 1 = \frac{3(k - 1)}{1} \\ 1 = 3(k - 1) \\ 1 = 3k - 3 \\ 1 + 3 = 3k \\ 4 = 3k \\ > > > > > > > > \frac{4}{3} = k < < < < < < < <$

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