Consider the system of quadratic equations y = 3x^2 – 5x, y = 2x^2 – x – c, where c is a real number. (a) For

Question

Consider the system of quadratic equations
y = 3x^2 – 5x,
y = 2x^2 – x – c,
where c is a real number.

(a) For what value(s) of c will the system have exactly one solution (x,y)?

(b) For what value(s) of c will the system have more than one real solution?

(c) For what value(s) of c will the system have no real solutions?

Solutions to the quadratics are (x,y) pairs. Your answers will be in terms of c, but make sure you address both x and y for each part.

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Bình An 4 years 2021-08-26T09:27:22+00:00 1 Answers 6 views 0

Answers ( )

  1. Helga
    0
    2021-08-26T09:28:51+00:00
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    9514 1404 393

    Answer:

      (a)  c = 4

      (b)  c < 4

      (c)  c > 4

    Step-by-step explanation:

    (a) The solutions to the system of equations can be found by substituting one expression for y into the other equation:

      3x^2 -5x = 2x^2 -x -c

      x^2 -4x +c = 0 . . . . . . . subtract the right side expression

    The discriminant is

      d = b^2-4ac = (4)^2 -4(1)(c) = 16-4c.

    The system will have exactly one solution when d = 0.

      16 -4c = 0

      4 -c = 0

    __

    (b) There will be more than one real solution when d > 0

      4 -c > 0

      c < 4 . . . . two real solutions

    __

    (c) There will be no real solutions when d < 0.

      4 -c < 0

      c > 4 . . . . no real solutions

    _____

    Additional comment

    The question posed here simply asks for a value of c. It does not ask for the solutions (x, y). We can count them without knowing exactly what they are.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )