Using the discriminant, determine the number of real solutions.
2x^2+7x-15=0

a. no real solutions
b. one real solution
c. two real solutions.

  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.

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.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

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