Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Answer:
Step-by-step explanation:
To find the solutions to the quadratic equation \( -3x^2 - 4x + 5 = 0 \) and express them in simplest radical form using the quadratic formula, we start by identifying the coefficients \( a = -3 \), \( b = -4 \), and \( c = 5 \).
The quadratic formula is:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Substitute the values of \( a \), \( b \), and \( c \) into the formula:
\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(-3)(5)}}{2(-3)} \]
Simplify the equation:
\[ x = \frac{4 \pm \sqrt{16 + 60}}{-6} \]
\[ x = \frac{4 \pm \sqrt{76}}{-6} \]
Now, simplify \( \sqrt{76} \):
\[ \sqrt{76} = \sqrt{4 \cdot 19} = 2\sqrt{19} \]
So the equation becomes:
\[ x = \frac{4 \pm 2\sqrt{19}}{-6} \]
Divide both terms in the numerator by -2:
\[ x = \frac{-2 \pm \sqrt{19}}{3} \]
Therefore, the solutions in simplest radical form are:
\[ x = \frac{-2 + \sqrt{19}}{3} \quad \text{and} \quad x = \frac{-2 - \sqrt{19}}{3} \]
Thus, the correct answer is:
\[ x = \frac{-2 \pm \sqrt{19}}{3} \]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
