the diffrence between the roots of the equation 2x^2-5x+c=0 is 0.25 find c

Question

the diffrence between the roots of the equation 2x^2-5x+c=0 is 0.25 find c

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RobertKer 5 years 2021-07-18T20:54:05+00:00 1 Answers 19 views 0

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  1. kiet
    0
    2021-07-18T20:55:15+00:00
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    Answer:

    • c = 3.09375

    Step-by-step explanation:

    Standard for of quadratic equation:

    • ax² + bx + c = 0

    We have

    • 2x² – 5x + c = 0

    Sum of the roots

    • x₁ + x₂ = – b/a = -(-5)/2 = 2.5

    Product of the roots

    • x₁x₂ = c/a = c / 2

    We have:

    • x₁ – x₂ = 0.25

    The square of the above is:

    • (x₁ – x₂)² = (x₁ + x₂)² – 4x₁x₂

    Substitute known values and solve for c:

    • 0.25² = (2.5)² – 4(c/2)
    • 2c = 6.25 – 0.0625
    • 2c = 6.1875
    • c = 3.09375

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