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​

Answer 1

To find the value of the square root part of the solution, you need to calculate the discriminant (the value inside the square root) which is b^2 - 4ac in the quadratic formula. In this case, a = 2, b = 7, and c = -15.

So, the discriminant = 7^2 - 4(2)(-15)
= 49 + 120
= 169

Now, you can plug this value back into your work:

x = (-7 ± √169) / 4
x = (-7 ± 13) / 4

Therefore, the two possible solutions for x are:
x = (-7 + 13) / 4 = 6/4 = 3/2
x = (-7 - 13) / 4 = -20/4 = -5