Question

question 3 (multiple choice worth 1 points)
(08.03 mc)
use the quadratic formula to find the exact solutions of ( x^2 - 5x - 2 = 0 )
( x = \frac{-b pm sqrt{b^2 - 4ac}}{2a} )
( circ x = \frac{5 pm sqrt{33}}{2} )
( circ x = \frac{-5 pm sqrt{33}}{2} )
( circ x = \frac{5 pm sqrt{17}}{2} )
( circ x = \frac{-5 pm sqrt{17}}{2} )

question 4 (multiple choice worth 1 points)
(08.03 mc)
when the solution of ( x^2 - 9x - 6 ) is expressed as ( \frac{9 pm sqrt{r}}{2} ), what is the value of ( r )?
( x = \frac{-b pm sqrt{b^2 - 4ac}}{2a} )
( circ 6 )
( circ 42 )
( circ 57 )
( circ 105 )

Explanation:

(Question 3):

Step1: Identify a, b, c values

For $x^2 - 5x - 2 = 0$, $a=1$, $b=-5$, $c=-2$

Step2: Compute discriminant $b^2-4ac$

$(-5)^2 - 4(1)(-2) = 25 + 8 = 33$

Step3: Substitute into quadratic formula

$x = \frac{-(-5) \pm \sqrt{33}}{2(1)} = \frac{5 \pm \sqrt{33}}{2}$

(Question 4):

Step1: Identify a, b, c values

For $x^2 - 9x - 6 = 0$, $a=1$, $b=-9$, $c=-6$

Step2: Compute discriminant $b^2-4ac$

$(-9)^2 - 4(1)(-6) = 81 + 24 = 105$

Step3: Match to given form

The discriminant equals $r$, so $r=105$

Answer:

Question 3: $\boldsymbol{x = \frac{5 \pm \sqrt{33}}{2}}$
Question 4: $\boldsymbol{105}$