Question

Алгебра 8 класс Решить через дискриминант 3x2-7x+4=0

Answer 1

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Answer 2

Solving the Quadratic Equation 3x^2 - 7x + 4 = 0

To solve the quadratic equation 3x^2 - 7x + 4 = 0 using the discriminant, we can follow these steps:

Step 1: Identify the coefficients of the quadratic equation. In this case, the coefficients are: - a = 3 - b = -7 - c = 4

Step 2: Calculate the discriminant (D) using the formula D = b^2 - 4ac. The discriminant helps determine the nature of the solutions. - D = (-7)^2 - 4 * 3 * 4 = 49 - 48 = 1 Step 3: Analyze the discriminant to determine the nature of the solutions: - If D > 0, the equation has two distinct real solutions. - If D = 0, the equation has one real solution (a perfect square). - If D < 0, the equation has no real solutions (complex solutions).

In this case, since D = 1, the equation has two distinct real solutions.

Step 4: Use the quadratic formula to find the solutions. The quadratic formula is given by: - x = (-b ± √D) / (2a)

Substituting the values from our equation, we have: - x = (-(-7) ± √1) / (2 * 3) - x = (7 ± 1) / 6

Simplifying further, we get: - x1 = (7 + 1) / 6 = 8 / 6 = 4 / 3 - x2 = (7 - 1) / 6 = 6 / 6 = 1

Therefore, the solutions to the quadratic equation 3x^2 - 7x + 4 = 0 are: - x1 = 4/3 - x2 = 1

I hope this helps! Let me know if you have any further questions.