SOLUTION: Write the quadratic equation whose roots are −4 and 3, and whose leading coefficient is 5.
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Question 924080: Write the quadratic equation whose roots are −4 and 3, and whose leading coefficient is 5.
Found 2 solutions by Theo, josmiceli:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the roots are x = -4 and 3, then the factors are (x+4) and (x-3)
your equation is (x+4)(x-3) = 0
multiply these factors out to get:
x^2 -3x + 4x - 12 = 0 which simplifies to:
x^2 + x - 12 = 0
multiply both sides of this equation by 5 to get:
5x^2 + 5x - 60 = 0
that's your equation.
the graph of that equation is shown below:
the equation that this was derived from has the same roots as shown below:
that's the graph of x^2 + x - 12 = 0
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
are solutions
The solutions are:
(1)
and
(2)
---------------------------
(1)
(2)
----------------------
Subtract (2) from (1)
(1)
(2)
-------------------------
and
(1)
(1)
(1)
-----------------
The equation is:
check:
Multiply both sides by
OK
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