Question

If
x=+5, is a root of the e equation
Kx²+13 x +10=0 then
complete the
activity and find value of k.​

Answer 1

Solution:

It is given that:

x = 5 is a root of the equation kx² + 13x + 10 = 0.

We have to find the value of the constant "k".

Solving:

$\sf{\longrightarrow\:f(x)=kx^2+13x+10}$

$\sf{\longrightarrow\:x=5}$

Putting the value of x into the equation:

$\sf{\longrightarrow\:0=k\times5^2+(13\times5)+10}$

$\sf{\longrightarrow\:0=k\times25+65+10}$

$\sf{\longrightarrow\:0=25k+75}$

$\sf{\longrightarrow\:0-75=25k}$

$\sf{\longrightarrow\:-75=25k}$

$\sf{\longrightarrow\:\dfrac{-75}{25}=k}$

$\sf{\longrightarrow\:-3=k}$

Therefore the value of k in the equation kx²+13x +10=0 is -3.

Note:

If we say that (x-1) is a factor of an expression f(x), then 1 is the value given to x and it helps to divide the equation evenly. When the expression is divided with the factor and leaves no remainder, it means that it has only one single factor.