Question

Suppose you are a solving a quadratic equation using the quadratic formula and this is your work so far. 2x^2 + 7x - 15= 0

`x=\frac{-7\ \pm\sqrt{\left(7\right)^{2}-4\left(2\right)\left(-15\right)}}{2\left(2\right)}`
`x=\frac{-7\ \pm\sqrt{???}}{4}`👈

What number goes in place ???

Answer 1

To fill in the ??? in the expression for the quadratic formula, we'll calculate the value of the discriminant, which is given by \( b^2 - 4ac \).

In your equation \( 2x^2 + 7x - 15 = 0 \):
- \( a = 2 \)
- \( b = 7 \)
- \( c = -15 \)

Now, plug these values into the discriminant formula:

\[
b^2 - 4ac = 7^2 - 4(2)(-15)
\]

Calculating \( 7^2 \):

\[
7^2 = 49
\]

Now calculating \( -4(2)(-15) \):

\[
-4(2)(-15) = 8 \times 15 = 120
\]

Now, combine these results:

\[
49 + 120 = 169
\]

So, the expression for the discriminant is \( 169 \). Therefore, the complete equation with the discriminant filled in is:

\[
x = \frac{-7 \pm \sqrt{169}}{4}
\]

Thus, the number that goes in place of ??? is \( 169 \).