Question

if x-a is the factor of 3x2- mx - nx than prove that a=m+n/3

Answer 1

See the solution in the link

Answer 2

Given,

• $(x-a)$ is a factor of $3x^2 -mx -nx$.

To find,

• We have to prove that $a = m+n /3$.

Solution,

This is proved that if x-a is the factor of 3x²- mx - nx then a=m+n/3.

We can simply prove that if x-a is the factor of 3x²- mx - nx then a=m+n/3.

It is given that x-a is a factor of $3x^2 -mx -nx$, then x = a must satisfies the given equation,

      $p(x) = 3x^2-mx-nx$

      $p(a) = 3(a)^2-m(a) -n(a)$

      $p(a) = 3a^2-ma -na$

If x-a is a factor of $3x^2 -mx -nx$ , then $p(a) = 3a^2-ma -na$ = 0, we get

     $3a^2-ma -na = 0$

Taking a common, we get

   $a(3a-m-n) = 0$

       $3a-m-n = 0$

         $3a = m+n$

           $a = m+n/3$

which is required to prove.

Hence proved that if x-a is the factor of 3x²- mx - nx then a=m+n/3.