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.
The teacher wrote this: x² + Ax + B
Joanie copies the quadratic onto her paper, but writes
down the wrong constant term (but the correct quadratic
and linear terms).
Joanie copied this: x² + Ax + C
She correctly factors the quadratic that she wrote down on
her paper, and determines that her quadratic has roots -16 and 2.
So Joanie got this: x=-16; x=2
So Joanie had this before: x+16=0; x-2=0
So Joanie had this factorization: (x+16)(x-2)
So Joanie copied: x²+14x-32
Since Joanie had the right linear term, A = 14,
so the teacher wrote this: x² + 14x + B
Kelvin copies the quadratic onto his paper, but he writes down
the wrong coefficient for the linear term (but the correct
quadratic and constant terms).
Kevin copied this: x² + Dx + B
He correctly factors the quadratic that he wrote down, and
determines that his quadratic has roots -36 and 2.
So Kevin got this: x=-36; x=2
So Kevin had this before: x+36=0, x-2=0
So Kevin had this factorization: (x+36)(x-2)
So Kevin copied: x²+34x-72
Since Kevin had the right constant term, B = -72
So the teacher wrote this: x² + 14x - 72
What are the roots of the quadratic that the teacher wrote
on the board?
I'll leave that last part up to you!!! Factor, set = 0, and
solve for the values of x, which are the roots.
Edwin
