Question

Which of the following are solutions to the equation below?

Check all that apply.

x^2 + 4x + 4 = 12

A. x =- √2+12
B. x = √2+12
C. x = -2√3-2
D. x = -2√3+2
E. x = 2√3-2
F. x = 2√3+2

Answer 1

There are several ways in which we could answer this question. My choice is to actually solve the given quadratic equation, x^2 + 4x + 4 = 12.

Note that x^2 + 4x + 4 is a perfect square. Thus,

x^2 + 4x + 4 = 12 is the same as (x+2)^2 = 12, so that

x+2 = plus or minus √3*√4, or plus or minus 2√3.

Thus, the two real, unequal roots are

x = -2 + 2√3 and x = -2 - 2√3. These correspond to answer choices C and E.

Answer 2

The two real, unequal roots are x = -2 + 2√3 and x = -2 - 2√3. These correspond to answer choices C and E.

what is a quadratic equation?

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Here we are having an equation:-

x ²+   4x   +   4   =   12

There are several ways in which we could answer this question. My choice is to actually solve the given quadratic equation,

x ²+   4x   +   4   =   12

Note that x ²+   4x   +   4   =   12  is a perfect square. Thus,

x ²+   4x   +   4   =   12

(  x  +  2  )²   =   12, so that

x  +  2 = plus or minus √3*√4, or plus or minus 2√3.

Thus, two real, unequal roots are x = -2 + 2√3 and x = -2 - 2√3. These correspond to answer choices C and E.

To know more about quadratic equations follow

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