Question

if x2+kx+6=(x+2)(x+3)for all x,value of k is?

Answer 1

2x+kx+6=(x+2)(x+3)
2x+kx+6=x^2+5x+6
X(2+k)+6-6=x(x+5)
X(2+k)=x(x+5)
2+k=x+5
By comparison
2=x
K=5

Answer 2

Answer:

Value of k = 5

Step-by-step explanation:

By algebraic identity :

$\boxed { (x+m)(x+n) = x^{2}+(m+n)x+mn}$

$Given \\x^{2}+kx+6 \\= (x+2)(x+3)\\=x^{2}+(2+3)x+2\times 3\\=x^{2}+5x+6$

Therefore,

$x^{2}+kx+6 = x^{2}+5x+6$

Compare both sides of the equation, we get

k = 5

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