Question

if x-2 is a factor of p(x) =2xsquare+3x-k then the vale of k is ​

Answer 1

Answer:

k = 14

Step-by-step explanation:

Given :

p(x) = 2x² + 3x - k

g(x) = x - 2

Said that g(x) is a factor of P(x).

To Find:

Value of 'k'.

Procedure:

Let's find the zero of g(x):-

$\sf \implies x - 2 = 0$

$\sf \implies x = 2$

Putting the value of x here:-

$\sf \implies p(x) = 2x^2 + 3x - k$

$\sf \implies p(1) = 2(2)^2 + 3(2) - k$

$\implies \sf p(1) = 8 + 6 - k$

$\implies \sf p(1) = 14 - k$

We know that g(x) is a factor of p(x), so is p(1).

From this information, we can infer that:-

$\implies \sf 14-k = 0$ (Because g(x) is factor of p(x).)

$\implies \sf -k = -14$

Value of k = 14

Answer 2

Given

• g(x) = X - 2

Given equation

• f(x) = 2x² + 3x - k

To find

• Value of k

Solution

$\rightarrow{x - 2 = 0}$

$\rightarrow{x = 2}$

Putting the value of x in the equation.

$\rightarrow{f(x) = 2x^2 + 3x - k}$

$\rightarrow{f(2) = 2×(2)^2 + 3×2 - k}$

$\rightarrow{f(2) = 8 + 6 - k}$

$\rightarrow{f(2) = 14 - k}$

Putting f(x) = 0

$\implies{14 - k = 0}$

$\implies{-k = -14}$

$\implies{k = 14}$