Question

Using the discriminant, determine the number of real solutions.

Answer 1

Answer:

  C.  two real solutions

Step-by-step explanation:

Your quadratic matches the form ...

  ax^2 +bx +c = 0

for the values a=2, b=7, c=-15.

The discriminant is ...

  d = b^2 -4ac

For your values of a, b, c, the discriminant value is ...

  d = 7^2 -4(2)(-15) = 169

The discriminant is positive, indicating there are two real solutions.

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When the discriminant is negative, there are no real solutions, only complex solutions.

When the discriminant is zero, there is one real solution.

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This equation factors as (2x-3)(x+5) = 0 and has solutions x=3/2, x=-5.