Question

If alpha and beta are zeros of polynomial 6x2 -5x-K and alpha -beta =7/6 then K=

With solutions

Answer 1

Step-by-step explanation:

$\alpha - \beta = \frac{ \sqrt{d} }{a} \\ {d} = {b}^{2} - 4ac \\ \: \: \: \: =( { - 5})^{2} - 4(6)( - k) \\ \: \: \: \: = 25 + 24k \\ \: \: \: \: = \sqrt{25 + 24k} \\ \alpha - \beta = \frac{ \sqrt{d} }{a} \\ \: \: \: \: \: \: \: \frac{7}{6} = \frac{ \sqrt{25 + 24k} }{6} \\ 42 = 6( \sqrt{25 + 24k)} \\ 7 = \sqrt{25 + 24k} \\ 49 = 25 + 24k \\ 49 - 25 = 24k \\ 24 = 24k \\ k = 1$