SOLUTION: A monic quadratic is a quadratic in which the coefficient of the quadratic term is 1. For example, r^2 - 3r + 7 is a monic quadratic, but 3t^2 - 3t + 1 is not.
A teacher writes
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Question 1018224: A monic quadratic is a quadratic in which the coefficient of the quadratic term is 1. For example, r^2 - 3r + 7 is a monic quadratic, but 3t^2 - 3t + 1 is not.
A teacher writes a monic quadratic on the board.
Joanie copies the quadratic onto her paper, but writes down the wrong constant term (but the correct quadratic and linear terms). She correctly factors the quadratic that she wrote down on her paper, and determines that her quadratic has roots -16 and 2.
Kelvin is factoring the same quadratic that the teacher wrote on the board. He also copies the quadratic onto his paper, but he writes down the wrong coefficient for the linear term (but the correct quadratic and constant terms). He correctly factors the quadratic that he wrote down, and determines that his quadratic has roots -36 and 2.
What are the roots of the quadratic that the teacher wrote on the board? (Write your answers in increasing order, separated by commas.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the first equation has roots of -16 and 2.
this means that the factors are (x+16) * (x-2).
multiply those factors out to get x^2 + 16x - 2x - 32.
combine like terms to get x^2 + 14x - 32.
the constant term is wrong.
this means the squared term and the linear term are both correct.
the squared term is x^2.
the linear term is 14x.
the second equation has roots of -36 and 2.
this means that the factors are (x+36) * (x-2).
multiply those factors out to get x^2 + 36x - 2x - 72.
combine like terms to get x^2 + 34x - 72.
the linear term is wrong.
this means the squared term and the constant term are both correct.
the squared term is x^2.
the constant term is -72.
put these two facts together and you get:
the correct squared term is x^2.
the correct linear term is 14x.
the correct constant term is -72.
the correct equation is x^2 + 14x - 72.
factor this equation to get (x-4) * (x+18).
the roots of this equation are x = 4 and x = -18.
the graph of the equation looks like this:
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