Question

if alpha and beta are the zero3s of polynomial x^2-5x+k such that alpha - beta =1 then find k

Answer 1

$\alpha + \beta = - b \div a \\ \alpha + \beta = 5 \div 1 \\ \alpha + \beta = 5.................(1)$
$\alpha \beta = c \div a \\ \alpha \beta = k$

$\alpha - \beta = 1.......(2)$
from 1 and 2 we get
$2 \alpha = 4 \\ \alpha = 2$
substituting in eq 1
$\beta = 3$
$product \: of \: roots = \alpha \beta \\ 5 \times k = 2 \times 3$
5k=6
k=6/5
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