Question:
Solve the quadratic equation:
\[
3x^2 - 11x = -10
\]
Solve the quadratic equation:
\[
3x^2 - 11x = -10
\]
Show Hint
Always check quadratic solutions against answer choices. Some tests intentionally add distractors that are close but not exact.
Updated On: Sep 30, 2025
- \(-2\)
- \(\frac{5}{3}\)
- \(3\)
- \(-\frac{5}{3}\)
- None of the other answers
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The Correct Option is C
Solution and Explanation
Step 1: Rearrange equation.
\[ 3x^2 - 11x + 10 = 0 \]
Step 2: Factorize.
We need two numbers whose product = \(3 \times 10 = 30\) and sum = \(-11\). \[ -6 \quad \text{and} \quad -5 \]
Step 3: Split middle term.
\[ 3x^2 - 6x - 5x + 10 = 0 \] \[ 3x(x - 2) - 5(x - 2) = 0 \] \[ (3x - 5)(x - 2) = 0 \]
Step 4: Solve roots.
\[ x = \frac{5}{3}, \quad x = 2 \] From the options, only \(x = 3\) is shown incorrectly, so the correct one matching is \(x = \frac{5}{3}\). But since the options are slightly mismatched, the closest valid solution from the given is \(\frac{5}{3}\).
Final Answer: \[ \boxed{\frac{5}{3}} \]
\[ 3x^2 - 11x + 10 = 0 \]
Step 2: Factorize.
We need two numbers whose product = \(3 \times 10 = 30\) and sum = \(-11\). \[ -6 \quad \text{and} \quad -5 \]
Step 3: Split middle term.
\[ 3x^2 - 6x - 5x + 10 = 0 \] \[ 3x(x - 2) - 5(x - 2) = 0 \] \[ (3x - 5)(x - 2) = 0 \]
Step 4: Solve roots.
\[ x = \frac{5}{3}, \quad x = 2 \] From the options, only \(x = 3\) is shown incorrectly, so the correct one matching is \(x = \frac{5}{3}\). But since the options are slightly mismatched, the closest valid solution from the given is \(\frac{5}{3}\).
Final Answer: \[ \boxed{\frac{5}{3}} \]
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