randRangeNonZero( -10, 10 ) randRangeNonZero( -10, 10 )
randRange(1,6)
SQUARE*A*B A*B SQUARE*(-A-B) -A-B

Determine where f(x) intersects the x-axis.

f(x) = plus(SQUARE + "x^2") + plus( LINEAR + "x" ) + CONSTANT

A
B

x = \quad\quad \text{and} \quad x = \quad

The two numbers -A and -B satisfy both conditions:

-A + -B = SIMPLELINEAR

-A \cdot -B = SIMPLECONSTANT

So (x + -A)(x + -B) = 0.

x + -A = 0 or x + -B = 0

Thus, x = A and x = B are the solutions.

SQUARE * A * A A * A SQUARE * ( -2 * A ) -2 * A

Determine where f(x) intersects the x-axis.

f(x) = plus( SQUARE + "x^2") + plus( LINEAR + "x" ) + CONSTANT

x = \quadA

The number -A used twice satisfies both conditions:

-A + -A = SIMPLELINEAR

-A \cdot -A = SIMPLECONSTANT

So (x + -A)^2 = 0.

x + -A = 0

Thus, x = A is the solution.

The function intersects the x-axis where f(x) = 0, so solve the equation:

plus( SQUARE + "x^2" ) + plus( LINEAR + "x") + CONSTANT=0

Dividing both sides by SQUARE gives:

x^2 + plus(SIMPLELINEAR + "x") + SIMPLECONSTANT=0

The coefficient on the x term is SIMPLELINEAR and the constant term is SIMPLECONSTANT, so we need to find two numbers that add up to SIMPLELINEAR and multiply to SIMPLECONSTANT.