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bluemoose604Lv1
22 Apr 2020
One method for determining the depth of a well is drop a stone into it and then measure the time it takes until the splash is heard. If
is the depth of the well of a quadratic equation from its coefficients. We can also obtain the coefficients from the solutions.
Find the solution of the solution the equation
and show that the product of the solutions is the constant term 20 and the sum of the solutions is 9, the negative of the coefficient of
.
Show that the same relationship between solutions and coefficients holds for the following equations:
![](data:image/png;base64,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)
Use the Quadratic formula to prove that in general, if the equation
has solutions
and
, then
and
.
One method for determining the depth of a well is drop a stone into it and then measure the time it takes until the splash is heard. If is the depth of the well of a quadratic equation from its coefficients. We can also obtain the coefficients from the solutions.
Find the solution of the solution the equation and show that the product of the solutions is the constant term 20 and the sum of the solutions is 9, the negative of the coefficient of
.
Show that the same relationship between solutions and coefficients holds for the following equations:
Use the Quadratic formula to prove that in general, if the equation has solutions
and
, then
and
.
Trinidad TremblayLv2
21 May 2020