Question

Suppose you are solving a quadratic equation using quadratic formula and this is your work so far:
2x^2 + 7x - 15 = 0
x = -7 ± √(7)^2 - 4(2)(-15)/2(2)
x = -7 ± √???/4

what number goes in place of ???

Answer 1

To find the number that goes in place of ??? in your expression, we need to calculate the discriminant of the quadratic equation using the formula:

\[
D = b^2 - 4ac
\]

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

Now, substituting these values into the formula:

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

Calculating each term:

1. \( (7)^2 = 49 \)
2. \( 4(2)(-15) = -120 \)

Now, substituting back into the discriminant formula:

\[
D = 49 - (-120) = 49 + 120 = 169
\]

So the expression under the square root in the quadratic formula becomes \( \sqrt{169} \).

Thus, the number that goes in place of ??? is **169**.

Your equation is now:

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