Question

Zeros of polynomial x square - 5 x + k such that a minus b equal to 1 find the value of k

Answer 1

Step-by-step explanation:

we know that,

sum of zeroes= -b/a

\alpha + \beta = 5

________________________(1)

also,

product of zeroes= c/a

\alpha \beta = k

_______________________(2)

Given:

\alpha - \beta = 1

______________________(3)

from (1) and (3)

\alpha + \beta = 5 \\ \alpha - \beta = 1 \ \: \: \: \: (on \: \: adding) \\ ................. \\ 2 \alpha = 6 \\ \\ \alpha = 3 \\ \\ put \: \: this \: \: in \: \: (3) \\ \\ 3 - \beta = 1 \\ \\ - \beta = - 2 \\ \\ \beta = 2

now put this value in (3)

\alpha \beta = k \\ \\ 2 \times 3 = k \\ \\ 6 = k