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

Question

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:

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