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 ???

1 answer

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=b24ac

In your equation 2x2+7x15=0, the coefficients are:

  • a=2
  • b=7
  • c=15

Now, substituting these values into the formula:

D=(7)24(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 169.

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

Your equation is now:

x=7±169/4