Question

find the value of k if (x-3) is a factor of x²-kx-2

Answer 1

If (x-3) is the factor of the given equation then even 3 must be a root of the given equation.

Let the roots of the equation be a and b.

Therefore,
Product of roots = Constant term / coefficient of x^2

a*b = -2
3*b=-2
b = -2/3

Now,
Sum of roots = -Coefficient of x / coefficient of x^2
3+(-2/3) = k
Therefore,
k = 7/3.

Hope this helps you !!

Answer 2

hello mate!.....

$given..... \\ x {}^{2} - kx - 2 = 0 \\ given \: one \: factor \: is \: x - 3 = 0 \\ x = 3 \: sub \: this \: value \: in \: bove \: eqn \\ 3 {}^{2} - k \times 3 - 2 = 0 \\ - 3k - 2 + 9 = 0 \\ - 3k = - 7 \\ k= \frac{7}{3}$
HOPE IT HELPS U DEAR......