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) About Me  (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:
graph%28600%2C600%2C-10%2C10%2C-70%2C70%2C5x%5E2+%2B+5x+-+60%29
the equation that this was derived from has the same roots as shown below:
graph%28600%2C600%2C-10%2C10%2C-70%2C70%2Cx%5E2+%2B+1x+-+12%29
that's the graph of x^2 + x - 12 = 0

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x+=+-4+
+x+=+3+
are solutions
+5x%5E2+%2B+b%2Ax+%2B+c+=+0+
The solutions are:
(1) +5%2A%28-4%29%5E2+%2B+b%2A%28-4%29+%2B+c+=+0+
and
(2) +5%2A3%5E2+%2B+b%2A3+%2B+c+=+0+
---------------------------
(1) +80+-+4b+%2B+c+=+0+
(2) +45+%2B+3b+%2B+c+=+0+
----------------------
Subtract (2) from (1)
(1) +80+-+4b+%2B+c+=+0+
(2) +-45+-+3b+-+c+=+0+
-------------------------
+35+-+7b+=+0+
+7b+=+35+
+b+=+5+
and
(1) +80+-+4%2A5+%2B+c+=+0+
(1) +80+-+20+%2B+c+=+0+
(1) +c+=+-60+
-----------------
The equation is:
+f%28x%29+=+5x%5E2+%2B+5b+-+60+
check:
+%28+x+-+3+%29%2A%28+x+%2B+4+%29+=+0+
+x%5E2+-+3x+%2B+4x+-+12+=+0+
+x%5E2+%2B+x+-+12+=+0+
Multiply both sides by +5+
+5x%5E2+%2B+5x+-+60+=+0+
OK