Question

Suppose you are a solving a quadratic equation using the quadratic formula and this is your work so far:


2x2+7x−15=0



x=
−7 ±72−42−15
22​



x=
−7 ±???
4​👈

What number goes in place of ???

Answer 1

To find the number that goes in place of ??? in your equation, we need to calculate the value inside the square root (the discriminant) of the quadratic formula.

The quadratic formula is given by:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the quadratic equation \(2x^2 + 7x - 15 = 0\):

- \(a = 2\)
- \(b = 7\)
- \(c = -15\)

Now, we need to calculate the discriminant \(b^2 - 4ac\):

1. Calculate \(b^2\):
\[
b^2 = 7^2 = 49
\]

2. Calculate \(4ac\):
\[
4ac = 4 \times 2 \times (-15) = -120
\]

3. Now, calculate \(b^2 - 4ac\):
\[
b^2 - 4ac = 49 - (-120) = 49 + 120 = 169
\]

Now you can replace ??? with \(\sqrt{169}\), since the discriminant is 169:

\[
\sqrt{169} = 13
\]

So in your equation, it should read:

\[
x = \frac{-7 \pm 13}{4}
\]

Thus, the number that goes in place of ??? is **13**.