+0

0
82
2

The quadratic x^2 + 5x + c = 0 has roots in the form of $x = \frac{-5 \pm \sqrt{17}}{2}$. What is the value of ?

Jun 28, 2021

#1
+234
+2

The quadratic formula is in format,

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

In this equation, $$x^2 + 5x + c = 0$$, a = 1, and b = 5, as we are given that. The only term in the formula that contains c is the discriminant, $$\sqrt{b^2-4ac} = \sqrt{17}$$

Square both sides,

$$b^2-4ac = 17$$

Plug in known values,

$$25-4c = 17$$

Subtract 25 on both sides and divide by -4 to get c = 2

Jun 28, 2021
#2
+121062
+2

THX,  Awesomeguy    !!!!

Here's another  method

By Vieta, the product of the roots  =  c

So   c =

(-5 + sqrt 17) /2   (  -5  -sqrt 17)  / 2   =

(25  - 17)  /  4   =

8 /  4   =  2

Jun 28, 2021