If ∝ and β are the roots of the quadratic equation x² – x – 2 = 0 then ∝² + β² is equal to​

Question

If ∝ and β are the roots of the quadratic equation x² – x – 2 = 0 then ∝² + β² is equal to​

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Tài Đức 5 years 2021-08-27T08:53:47+00:00 2 Answers 30 views 0

Answers ( )

  1. niczorrrr
    0
    2021-08-27T08:54:47+00:00
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    Answer:

    α² + β² = 5

    Step-by-step explanation:

    Given a quadratic equation in standard form

    ax² + bx + c = 0 ( a≠ 0 ) , then

    sum of roots = – \frac{b}{a}

    product of roots = \frac{c}{a}

    x² – x – 2 = 0 ← is in standard form

    with a = 1, b = – 1, c = – 2 , then

    α + β = – \frac{-1}{1} = 1

    αβ = \frac{-2}{1} = – 2

    Using the identity

    (α + β)² = α² + β² + 2αβ , then

    α² + β² = (α + β)² – 2αβ = 1² – 2(- 2) = 1 + 4 = 5

  2. thongdat2
    0
    2021-08-27T08:55:45+00:00
    Reply

    Answer :

    \large \boxed{ \boxed{\mathrm{ \alpha }^{2} + { \beta }^{2} = 5}}

    Given :

    • \alpha + \beta = 1
    • \alpha \times \beta = - 2

    let’s solve for :

    • { \alpha }^{2} + { \beta }^{2}
    • { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta - 2 \alpha \beta
    • ( \alpha + \beta ) {}^{2} - 2 \alpha \beta

    let’s plug the values,

    • (1) {}^{2} -2 \times ( - 2)
    • 1 + 4
    • 5

    \mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}

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