Question

Q1.If x² - kx - 6 = (x - 6) (x + 1) forall x, then the value of k is​

Answer 1

Step-by-step explanation:

Given:

x²-kx-6= (x-6)(x+1)

To find:

we have to find the value of x

SOLUTION:

x²-kx-6= (x-6)(x+1)

Firstly expanding the terms and opening the brackets on the LHS

=> x²-kx-6= x( x+1)-6(x+1)

=> x²-kx-6= x²+x-6x-6

=> x²-kx-6= x²-5x-6

we see on both sides quadratic equation is formed .

Now , comparing the coefficient of x on both sides because we have to find the value of x and on the right side k is the coefficient of x.

after comparing,we get -k= -5

k= 5

Check

x²-kx-6

=>x²-5x-6 which is equal to the RHS

Answer 2

$\huge \fcolorbox{red}{orange}{ \bf \color{maroon}{k = 5}}$

Step-by-step explanation:

QUESTION :-

If x² - kx - 6 = (x - 6)(x + 1) for all x, then the value of k is

_____________________

SOLUTION :-

Let's simplify the RHS of equation [we will use distributive property]

.

RHS -

$\bf(x - 6)(x + 1) \\ \bf = x(x + 1) - 6(x + 1) \\ \bf = {x}^{2} + x - 6x - 6 \\ \bf = {x}^{2} - 5x - 6$

.

Now,

LHS = RHS

$\bf = > {x}^{2} - kx - 6 = {x }^{2} - 5x - 6 \\ \bf = > - kx - 6 = {x}^{2} - {x}^{2} - 5x - 6 \\ \bf = > - kx = - 5x - 6 + 6 \\ \bf = > - kx = - 5x \\ \bf = > - k = \frac{ - 5 \cancel{x}}{ \cancel{x}} \\ \bf = > - k = - 5 \\ \bf = > k = 5$

So,

the value of k is 5 .

.

Hope it helps.