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Find the discriminant of the equation $x^2+4x+4$

Step-by-step Solution

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Final answer to the problem

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Step-by-step Solution

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The discriminant (D) of a quadratic polynomial of the form $ax^2+bx+c$ is calculated using the following formula, where $a$, $b$ and $c$ are the coefficients of the corresponding terms

$D=b^2-4ac$
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From the equation, we see that $a=1$, $b=4$ and $c=4$. Replacing the values of $a$, $b$ and $c$ in the previous formula, we obtain

$D=4^2+4\cdot 1\cdot -4$
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Multiply $4$ times $1$

$4^2+4\cdot -4$
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Multiply $4$ times $-4$

$4^2-16$
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Calculate the power $4^2$

$16-16$
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Subtract the values $16$ and $-16$

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The discriminant of the polynomial results in

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Final answer to the problem

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Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyFactorFactor by completing the squareFind the integralFind the derivativeFind x^2+4x using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even points

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Main Topic: Discriminant of Quadratic Equation

Quadratic equations are those algebraic equations of the form ax^2+bx+c, where a, b, and c are constant values. The discriminant of a quadratic equation is calculated using the formula D=b^2-4ac, and it helps us to determine how many roots an equation of this type has. When D>0 the equation has two real roots, when D<0 the equation has no real roots, and when D=0 the equation has a repeated real root.

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