Question

Find the value of k, if x - 1 is a factor of p(x) in each of the following case :-
p(x) = kx² - 3x + k

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Answer 1

Answer:

k = 3/2

Step-by-step explanation:

It is given that we need to find the value of k when x-1 is a factor of p(x).

Factor of p(x) :- What hint does it give us?

This means that we need to place the value of x such that the value of k is easily known.

As, x-1 is a factor of kx² - 3x + k, so that means the remainder is zero, right?

Apply remainder theorem in this case:-

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x-1 = 0

x +1 - 1 = 0 +1

x = +1

So, we can substitute the values and make the equation as:-

kx² - 3x + k = 0

k(1)² - 3(1) + k = 0

k - 3 + k = 0

2k - 3 = 0

2k = + 3

k = $\dfrac{3}{2}$

So, k = 3/2 is the required answer to the above question.

Answer 2

Question :-

Find the value of k, if x - 1 is a factor of p(x) in each of the following case :-

p(x) = kx² - 3x + k

Solution :-

$p(x) = k {x}^{2} - 3x + k$

kx² - 3x + k = 0

k(1)² - 3(1) + k = 0

k - 3 + k = 0

2k - 3 = 0

2k = + 3

k = $\sf\dfrac{3}{2}$

✓ Therefore, we can see that the value of k will be $\Large \sf \frac{3}{2}$.