Question

if m and n are the zeros of polynaomial ax-5x+c find a and c .if m+n=mn=10

Answer 1

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$


$\underline{ \bf{Given : }}$


'm' and 'n' are the zeroes of :
$p(x) = \: a {x}^{2} - 5x + c$

It is also given that,

m + n = mn = 10.


$\underline{ \bf{To \: Find :}}$

The value of 'a' and 'c'.


$\underline{ \bf{Process :}}$


We know,

$Sum \: of \: the \: zeroes = \: \frac{ - b}{a}$

$= > \: m \: + \: n \: = \: - (\frac{ - 5}{a} )$

$= > \: 10 \: = \: \frac{5}{a} \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( \bf{from \: given})$

$= > \: a \: = \: \frac{5}{10}$

$= > \: a \: = \: \frac{1}{2}$


and


$Product \: of \: the \: zeroes = \frac{c}{a}$

$= > \: m \: \times \: n \: = \: \frac{c}{a}$

$= > \: 10 \: = \: \frac{c}{a} \: \: \: \: \: \: \: \: \: \: \: \: \: (\bf{from \: given})$

Putting the value of 'a' from above equation, we get

$= > \: 10 \: = \: \frac{c}{ (\frac{1}{2}) }$

$= > \: 10 \: = 2c$

$= > \: c \: = \: 5$


So, we got the value of 'a' and 'c' , which are :

$\boxed{ \: \: \: \bf{ \: a \: = \frac{1}{2} \: \: \: \: \: \: and \: \: \: \: \: b \: = \: 5 \: \: \: \: }}$