Question

Which phrase correctly describes the solution to the quadratic equation?
2x2 + 25 = -x2 + 10x
exactly one real solution
infinitely many solutions
two complex solutions
two real solutions

Answer 1

Answer:

Step-by-step explanation:

hello :

2x² + 25 = -x² + 10x

2x²+x²-10x+25 =0

3x²-10x+25=0

∆ = b²- 4ac      a=3  and  b=-10   and  c=25

∆ = (-10)²- 4(3)(25)=100 -300 = -200< 0

two complex solutions

Answer 2

Answer:

two complex solutions

Step-by-step explanation:

Rewrite the equation in standard form by combining like terms and setting the equation equal to zero:

 

        2x² + 25 = -x² + 10x

3x² – 10x + 25 = 0

 

Identify the values of a, b, and c:

a = 3, b = -10, c = 25

 

Evaluate the discriminant:

b² – 4ac = (-10)² – 4(3)(25)

             = -200

The value of the discriminant is -200. Because the discriminant is negative, the equation has no real solution, which means it has two complex solutions.