Math Problem Statement

2x²-7x+3

Solution

To solve the quadratic equation 2x27x+3=02x^2 - 7x + 3 = 0, we can use the quadratic formula:

x=b±b24ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Here, a=2a = 2, b=7b = -7, and c=3c = 3. Plugging these values into the quadratic formula, we get:

x=(7)±(7)242322x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 2 \cdot 3}}{2 \cdot 2} x=7±49244x = \frac{7 \pm \sqrt{49 - 24}}{4} x=7±254x = \frac{7 \pm \sqrt{25}}{4} x=7±54x = \frac{7 \pm 5}{4}

This gives us two solutions:

x=7+54=124=3x = \frac{7 + 5}{4} = \frac{12}{4} = 3 x=754=24=12x = \frac{7 - 5}{4} = \frac{2}{4} = \frac{1}{2}

Therefore, the solutions to the quadratic equation 2x27x+3=02x^2 - 7x + 3 = 0 are x=3x = 3 and x=12x = \frac{1}{2}.

Would you like more details or have any questions?

Here are 8 relative questions to expand your understanding:

  1. How do you factor a quadratic equation if it can be factored?
  2. What is the discriminant, and how does it determine the nature of the roots of a quadratic equation?
  3. Can you solve a quadratic equation using the method of completing the square?
  4. How do you graph a quadratic function and identify its vertex?
  5. What is the importance of the axis of symmetry in a quadratic function?
  6. How do you find the maximum or minimum value of a quadratic function?
  7. How can quadratic equations be applied in physics and engineering problems?
  8. What are the properties of the roots of a quadratic equation when the discriminant is zero or negative?

Tip: Always check if the quadratic equation can be factored easily before using the quadratic formula, as factoring can sometimes provide a quicker solution.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Quadratic Formula

Formulas

Quadratic formula

Theorems

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Suitable Grade Level

High School