SOLUTION: Write a quadratic equation with -1/3 and 4 as its roots. Write the equation in standard form.

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Question 1029543: Write a quadratic equation with -1/3 and 4 as its roots. Write the equation in standard form.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-%28-1%2F3%29%29%28x-4%29=0, rawest form;
%28x%2B1%2F3%29%28x-4%29=0-------factored form.

One way to get standard form is find the vertex point which is exactly in the middle of the two given & known roots.

%28-1%2F3%2B4%29%2F2
%28-1%2F3%2B12%2F3%29%2F2

%2811%2F3%29%2F2

11%2F6-------coordinate for the vertex, x value.

y=%2811%2F6%2B1%2F3%29%2811%2F6-4%29
y=%2811%2F6%2B2%2F6%29%2811%2F6-36%2F6%29
y=%2813%2F6%29%28-25%2F6%29
y=-325%2F36--------y coordinate of the vertex.

Plug in to standard purely variablized form.
y=1%28x-h%29%5E2%2Bk, in which a=1;
highlight%28y=%28x-11%2F6%29%5E2-325%2F36%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Write a quadratic equation with -1/3 and 4 as its roots. Write the equation in standard form.
Since x+=+-+1%2F3 is a root, then x+%2B+1%2F3+=+0, or 3x+%2B+1+=+0 is a factor

Since x = 4 is a root, then x - 4 = 0 is a factor

We can then say that: (3x + 1)(x - 4) = 0

After FOILing the binomials, we get: highlight_green%283x%5E2+-+11x+-+4+=+0%29 ------ Quadratic equation, in standard form