Question

2.

How can you tell when a quadratic equation has two identical, rational solutions? (1 point)

when the radicand is negative
when b in the quadratic formula is greater than the radicand
when the radicand equals zero
when the radicand is not a perfect square,

Answer 1

The general formula for the solutions of a quadratic equation
ax² + bx + c = 0

are given by:

x₁₂ = [- b +- √(b²-4ac) ] / 2a

You have three cases:

1) the radicand is positive: you then have two dinstinct soutions, one with the root added to (-b) and then divided by 2a, and the other one with the root subtracted to (-b) and then divided by 2a.

2) the radicand is negative: you then have no solutions, because the root can't be performed. This case means that the given polynomial is never equal to zero.

3) the radicand is equal to zero: you then have the same value for both the solutions, which is -b/(2a).

Therefore your answer should be: C) when the radicand is equals to zero.