Question

question 8 (multiple choice worth 1 points)
(08.03 mc)
use the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, to solve the equation $3x^2 + 4x - 2 = 0$. round to the nearest hundredths
\\(\bigcirc\\) $x = -0.39$ and $x = 1.72$
\\(\bigcirc\\) $x = -5.41$ and $x = -2.59$
\\(\bigcirc\\) $x = -1.72$ and $x = 0.39$
\\(\bigcirc\\) $x = -10.32$ and $x = 2.32$

question 9 (multiple choice worth 1 points)
(08.03 mc)
the quadratic equation $4x^2 + 45x + 24 = 0$ was solved using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
one solution is $-10.69$. what is the other solution? round to the hundredths place.
\\(\bigcirc\\) $0.51$
\\(\bigcirc\\) $10.69$
\\(\bigcirc\\) $-1.12$
\\(\bigcirc\\) $-0.56$

Explanation:

Step1: Identify a, b, c for Q8

For $3x^2 + 4x - 2 = 0$, $a=3$, $b=4$, $c=-2$

Step2: Calculate discriminant for Q8

$\sqrt{b^2-4ac} = \sqrt{4^2 - 4(3)(-2)} = \sqrt{16+24} = \sqrt{40} \approx 6.3246$

Step3: Compute roots for Q8

$x = \frac{-4 \pm 6.3246}{2(3)}$
First root: $\frac{-4 + 6.3246}{6} \approx \frac{2.3246}{6} \approx 0.39$
Second root: $\frac{-4 - 6.3246}{6} \approx \frac{-10.3246}{6} \approx -1.72$

Step4: Identify a, b, c for Q9

For $4x^2 + 45x + 24 = 0$, $a=4$, $b=45$, $c=24$

Step5: Use sum of roots property for Q9

Sum of roots: $x_1 + x_2 = -\frac{b}{a} = -\frac{45}{4} = -11.25$

Step6: Solve for second root of Q9

Let $x_1=-10.69$, then $x_2 = -11.25 - (-10.69) = -0.56$

Answer:

Question 8: $\boldsymbol{x = -1.72}$ and $\boldsymbol{x = 0.39}$
Question 9: $\boldsymbol{-0.56}$