Answer:
The quadratic equation x2 + 8x + 16 = 0 is a perfect square trinomial, which means it can be factored as (x+4)²=0. Therefore, the nature of the quadratic equation is a perfect square trinomial, and it has one real root with a multiplicity of 2.
The quadratic equation x2 - 24x + 144 = 0 can be factored as (x-12)²=0, which is also a perfect square trinomial. Therefore, the nature of the solutions is a perfect square trinomial, and it has one real root with a multiplicity of 2.
The quadratic equation x2 - 25 = 0 can be factored as (x+5)(x-5)=0, which means it has two real roots: x=5 and x=-5.
The quadratic formula determines the solutions to the quadratic equation in terms of its coefficients. The formula is x = (-b ± √(b²-4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
The roots of the quadratic equation 2x2 + 5x + 3 = 0 can be found by factoring it as (2x+3)(x+1)=0, which means the roots are x=-3/2 and x=-1.
Explanation: