Question

What is the maximum value of k if the polynomial x2 – 3x + k can be written as the product of two first degree polynomials.

Answer 1

Step-by-step explanation:

x²-3x+k

Now -3x can be only written as= -x-2x

Now We split the middle term.Put it

x²-x-2x+k

x(x-1)-2(x-k)

Why We take -2 as common as to make two 1 degree terms .

So what should I place on k in

x(x-1)-2(x-k) so that X-k=x-1

We should place 2 on place of k.

as -2x+2(k)

=-2(x-1)

So,

x(x-1)-2(x-1)

(x-2)(x-1)

Check.

(x-2)(x-1)

x²-x-2x+2

x²-3x+2

Comparing with x²-3x+k

k=2

Maximum Value of K should be=2

Answer 2

Answer:

Maximum value of k should be 2

Step-by-step explanation:

Given Problem:

What is the maximum value of k if the polynomial x2 – 3x + k can be written as the product of two first degree polynomials.

Solution:

To Find:

The maximum value of k.

---------------

Method:

x²-3x+k

Now,

-3x can only be written as:

$=>\sf -x-2x$

Now,

Split the middle term:

$=>x^2-x-2x+k$

$=>x(x-1)-2(x-k)$

We take -2 as common as to make two 1 degree terms.

So,

$=>x(x-1)-2(x-k) So,\: that\: x-k=x-1$

Now,

We have place 2 on place of k.

$=>-2x+2(k)$

$=>-2(x-1)$

So,

$=>x(x-1)-2(x-1)$

$=>(x-2)(x-1)$

Now,

Checking:

$=>(x-2)(x-1)$

$=>x^2-x-2x+2$

$=>x^2-3x+2$

Now,

Comparing with x²-3x+k

k = 2

Hence,

It implies that value of k should be 2