Input three numbers to check if they form a perfect square trinomial.
A quadratic equation is a perfect square trinomial if its discriminant \(b^2 - 4ac\) equals zero. This means the equation has exactly one real root, corresponding to a parabola that touches the x-axis at a single point.
Solution:
Identify Coefficients: \(a = 1\), \(b = 30\), \(c = 256\)
Calculation: \(b^2 - 4ac = 30^2 - 4 \times 1 \times 256 = 900 - 1024 < 0\)
Result: Since \(b^2 - 4ac < 0\), this is not a perfect square trinomial.
Solution:
Identify Coefficients: \(a = 4\), \(b = -20\), \(c = 25\)
Calculation: \(b^2 - 4ac = -20^2 - 4 \times 4 \times 25 = 400 - 400 = 0\)
Result: Since \(b^2 - 4ac = 0\), this is a perfect square trinomial.