Question

Given that m + 2, where m is a positive integer, is a zero of the polynomial q(x) = x²-mx-6.
Which of these is the value of m?​

Answer 1

GIVEN :-

m+2 is a zero of polynomial ,

Q(x) = x^2 - mx - 6

TO FIND :-

Value of m

SOLUTION:-

==> x^2 - mx - 6 = 0   .................................(1)

Put the zero of the polymomial in equation (1),

==> (m+2)^2 - m(m+2) - 6 = 0

==>  m^2 + 4 + 4m - m^2 -2m - 6 = 0

==>  2m - 2 = 0

==> m = 2/2

==> m = 1

So, the value of m is 1

Answer 2

Given,

Polynomial, $\[q\left( x \right) = {x^2} - mx - 6\]$

Zero of polynomial $\[ = m + 2\]$

Solution,

Zero of any polynomial satisfy the given polynomial. So replace x with m+2.

$\[\begin{array}{l}{x^2} - mx - 6 = 0\\ \Rightarrow {\left( {m + 2} \right)^2} - m\left( {m + 2} \right) - 6 = 0\\ \Rightarrow {m^2} + 4m + 4 - {m^2} - 2m - 6 = 0\\ \Rightarrow 2m - 2 = 0\\ \Rightarrow m = 1\end{array}\]$

Hence the value of m is 1.