A portion of the Quadratic Formula proof is shown. Fill in the missing statement. Statements Reasons x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c all over 4 times a squared plus b squared over 4 a squared Find a common denominator on the right side of the equation x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation the quantity x plus b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Rewrite the perfect square trinomial on the left side of the equation as a binomial squared ? Take the square root of both sides of the equation x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c end quantity, all over 4 times a squared x plus b over 2 times a all squared equals plus or minus b squared minus 4 times a times c, all over 4 times a squared all squared the square root of x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared

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The answer should be x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c end quantity, all over 4 times a squared. To answer look at the chart that will help make sure you get the correct answer.

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The answer should be x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over 4 times a squared.

What is a quadratic equation?

A quadratic equation is a second-degree algebraic equation in x. The conventional form of the quadratic equation is ax2 + bx + c = 0, with a and b as coefficients, x as the variable, and c as the constant component.

What are the roots of a quadratic equation?

The values of variables satisfying the given quadratic equation are called its roots.

Let the quadratic equation be:

ax^2 + bx + c = 0

ax^2 + bx = -c (subtract c from both sides)

x^2 + (b/a)x = -c/a

x^2 + (b/a)x + (b/2a)^2 = -c/a + (b/2a)^2

x^2 + (b/a)x + (b^2/4a^2) = (b^2-4ac)/4a^2

(x + b/2a)^2 = (b^2 - 4ac)/4a^2

x + b/2a = + ((b^2 - 4ac)^(1/2))/2a.......(1)

x + b/2a = - ((b^2 - 4ac)^(1/2))/2a........(2)

x = (-b + ((b^2 - 4ac)^(1/2)))/2a or x = (-b - ((b^2 - 4ac)^(1/2)))/2a

Hence the two roots of the equation are x = (-b + ((b^2 - 4ac)^(1/2)))/2a and x = (-b - ((b^2 - 4ac)^(1/2)))/2a respectively.

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