Question

if m and n are zeros x power 2-5x+k and m-n=1, then find the value of k. ​

Answer 1

$\textbf{Given:}$

$\text{m and n are zeros of x^2-5x+k and m-n=1}$

$\textbf{To find:}$

$\text{The value of k}$

$\textbf{Solution:}$

$\text{Consider,}\;x^2-5x+k$

$\text{Then,}$

$\textbf{Sum of the zeros = \dfrac{-b}{a} }$

$\implies\,m+n=\dfrac{5}{1}$

$\implies\,m+n=5$

$\textbf{product of the zeros = \dfrac{c}{a} }$

$\implies\,m\,n=\dfrac{k}{1}$

$\implies\,m\,n=k$

$\text{Now,}$

$\bf\,(m+n)^2=(m-n)^2+4\,mn$

$(5)^2=(1)^2+4\,k$

$25=1+4\,k$

$24=+4\,k$

$\implies\,k=\frac{24}{4}$

$\implies\bf\,k=6$

$\therefore\textbf{The value of k is 6}$

Find more:

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