Roots of polynomials

Roots of polynomials Quiz

Spec 4.1–2 · Edexcel A-Level Further Maths: Quiz

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  1. 1. The cubic 3x3+6x2−4x+9=03x^3+6x^2-4x+9=0 has roots α,β,γ\alpha,\beta,\gamma. Find αβγ\alpha\beta\gamma.

    • A. 33
    • B. −3-3
    • C. −2-2
    • D. −43-\frac43

  2. 2. The cubic x3−3x2−2x+1=0x^3-3x^2-2x+1=0 has roots α,β,γ\alpha,\beta,\gamma. Find α2+β2+γ2\alpha^2+\beta^2+\gamma^2.

    • A. 55
    • B. 99
    • C. 1111
    • D. 1313

  3. 3. The cubic x3+px2+qx+r=0x^3+px^2+qx+r=0 has roots α,β,γ\alpha,\beta,\gamma. Which expression equals 1α+1β+1γ\frac1\alpha+\frac1\beta+\frac1\gamma?

    • A. −qr-\frac qr
    • B. qr\frac qr
    • C. −pr-\frac pr
    • D. rq\frac rq

  4. 4. The roots of x3−6x2+11x−6=0x^3-6x^2+11x-6=0 are doubled. Which equation has the new roots?

    • A. y3−6y2+11y−6=0y^3-6y^2+11y-6=0
    • B. y3−12y2+22y−12=0y^3-12y^2+22y-12=0
    • C. y3−12y2+44y−48=0y^3-12y^2+44y-48=0
    • D. y3−6y2+22y−48=0y^3-6y^2+22y-48=0

  5. 5. The quartic x4−5x3+2x2−x+7=0x^4-5x^3+2x^2-x+7=0 has roots α,β,γ,δ\alpha,\beta,\gamma,\delta. Find ∑αβγ\sum\alpha\beta\gamma.

    • A. −1-1
    • B. 11
    • C. 55
    • D. 77

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