Math

Question Find the discriminant of the quadratic function f(x)=x2+8x15f(x) = x^2 + 8x - 15.

Studdy Solution

STEP 1

Assumptions1. The function is a quadratic function of the form f(x)=ax+bx+cf(x) = ax^ + bx + c . The coefficients are a=1a =1, b=8b =8, and c=15c = -15
3. The discriminant of a quadratic function is given by =b4ac = b^ -4ac

STEP 2

First, we need to find the discriminant of the function. We can do this by substituting the coefficients into the formula for the discriminant.
=b24ac = b^2 -4ac

STEP 3

Now, plug in the given values for the coefficients aa, bb, and cc to calculate the discriminant.
=82(1)(15) =8^2 -(1)(-15)

STEP 4

Calculate the discriminant.
=64(60) =64 - (-60)

STEP 5

implify the expression to find the discriminant.
=64+60=124 =64 +60 =124The discriminant of the function f(x)=x2+8x15f(x)=x^{2}+8 x-15 is124.

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