Find the zeros of polynomial 4m² 8m8m

$4 \exponential{m}{2} + 8 m = 0 $

Steps Using the Quadratic Formula

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To find equation solutions, solve m=0 and 4m+8=0.

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

m=\frac{-8±\sqrt{8^{2}}}{2\times 4}

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

Take the square root of 8^{2}.

Now solve the equation m=\frac{-8±8}{8} when ± is plus. Add -8 to 8.

Now solve the equation m=\frac{-8±8}{8} when ± is minus. Subtract 8 from -8.

The equation is now solved.

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

\frac{4m^{2}+8m}{4}=\frac{0}{4}

m^{2}+\frac{8}{4}m=\frac{0}{4}

Dividing by 4 undoes the multiplication by 4.

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

Factor m^{2}+2m+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

\sqrt{\left(m+1\right)^{2}}=\sqrt{1}

Take the square root of both sides of the equation.

Subtract 1 from both sides of the equation.