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Use discriminant to determine the number and type of solutions to the following quadratic equations 2x² - 2x +3 = 0

User LazR
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Answer:

Number of solutions: 0

Type of solutions: Nonreal

Explanation:

Identifying the form of 2x^2 - 2x + 3 = 0

2x^2 - 2x + 3 = 0 is in the standard form of a quadratic, whose general equation is given by:

ax^2 + bx + c = 0, where

  • a, b, and c are constants.

Thus, 2 is our a value, -2 is our b value, and 3 is our c value.

Using the discriminant to determine the number and type of solutions:

The discriminant (D) comes from the quadratic formula and is given by:

D = b^2 - 4ac

The discriminant can reveal three things about the number and type of solutions:

  • When D < 0, there are 0 real solutions.
  • When D = 0, there is 1 real solution.
  • When D > 0, there are 2 real solutions.

Thus, we can plug in -2 for b, 2 for a, and 3 for c in the discriminant equation to determine the number and type of solutions for 2x^2 - 2x + 3 = 0:

D = (-2)^2 - 4(2)(3)

D = 4 -24

D = -20

Since -20 is less than 0, there are 0 real solutions.

User Imekon
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