Question

Find the value of k if x + 2 is a factor of 2x2 + kx + 4​

Answer 1

Answer:

k = 6

Step-by-step explanation:

We have to find value of k

Given :

$\large p(x)=2x^2 + kx + 4\ and \ g(x)=x+2$

Zeroes of g (x) = x + 2 = 0

x = - 2

Now putting x = -2 in p ( x )

$\large p(x)=2x^2 + kx + 4\\\\\\\large p(-2)=2(-2)^2 + k\times-2 + 4=0\\\\\\\large p(-2)=2\times4-2k+ 4=0\\\\\\\large 12-2k=0\\\\\\\large 12=2k\\\\\\\large k=6$

Thus we get k = 6

Answer 2

Question :-

Find the value of k if (x+2) is a factor of 2x²+kx+4

Solution :-

Here, f(x)= 2x²+kx+4

Divided by the linear polynomial (x+2)

At first, we will find out the zero of polynomial (x+2)

=> x+2 = 0

=> x = - 2

f(x)=2x²+kx+4 divided by (x+2) gives the remainder 0. And f(-2) :-

=> 2×(-2)²+k×(-2)+4 = 0

=> 2×4+(-2k)+4 = 0

=> 2×(-2)²+k×(-2)+4 = 0

=> 2×4+(-2k)+4 = 0

=> 8 - 2k + 4 = 0

=> - 2k = - 12

=> 2k = 12

=> k = 12/2

=> k = 6

Hence, the value of k is 6.