Question

For what positive integers $c$, with $c < 100$, does the following quadratic have rational roots? \[ 3x^2 + 20x + c \]

Answer 1

The positive integer c for the expression to have a rational root is 8

Calculate the rational root of a function

For a quadratic equation to have a rational root, then;

$b^2-4ac =0$

From the given equation;

a = 3

b = 20

Substitute into the equation above to have:

20^2-4(3)c = 0

400 - 12c = 0

12c =100

c = 100/12

c= 8.3

Hence the positive integer c for the expression to have a rational root is 8

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