A: what are the solutions to the quadratic equation
x^2 +4=0?
b: what is the factored form of the quadratic equation x^2+4?

The correct answer for question A is x=2i or x= -2i

The correct answer for question B is (x+2i)(x-2i)

Step-by-step explanation:

Solution of question A:

x²+4=0

Subtract 4 from both sides.

x²+4-4=0-4

x²=-4

Take square root of both sides

√x²=+/-√-4

We know that i=√-1

So,

x=+/-(√4)(√-1)

x=+/-2i

Therefore x= 2i, x= -2i

Solution of question B:

x²+4

It cannot be factored using real number coefficient. You have to use complex numbers.

As we know -4 =(2i)², so we can write as:

x²+4=x² - (-4)= x²-(2i)²

Now factor using the difference of squares:

x²+4=(x+2i) (x-2i)

sup

step-by-step explanation:

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!