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How do you find the roots, real and imaginary, of #y=-x^2 + 24x +4(x/2-1)^2 # using the quadratic formula?

Answer 1

Hazel Anglin

There are no roots as the expression is not a true quadratic

Expand and simplify the expression #y = -x^2 +24x +4(x^2/4 -x +1)# #y = 20x +4#

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Answer 2

Hazel Anglin

To find the roots of the quadratic equation ( y = -x^2 + 24x + 4\left(\frac{x}{2} - 1\right)^2 ), first rewrite the equation in standard form ( ax^2 + bx + c = 0 ), where ( a ), ( b ), and ( c ) are coefficients.

After simplifying, the equation becomes ( y = -x^2 + 24x + x^2 - 8x + 4 ).

Combine like terms to get ( y = 16x + 4 ).

Now, set ( y ) equal to 0 to solve for ( x ), so ( 0 = 16x + 4 ).

Solve for ( x ) to get ( x = -\frac{1}{4} ).

This is a linear equation, not a quadratic one. Therefore, there's only one root.

The root of the given equation is ( x = -\frac{1}{4} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.