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IB Mathematics: Applications and Interpretation HL · 12.4: Solving Equations with Technology · 12.4.3

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Polynomial equations with the solver Problem set B

Rearrange to polynomial form first. Use the polynomial solver, and give real roots to 3 significant figures.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. Solve \(x^3-3x^2=4x-2\).

  2. Find the real roots of \(x^4-7x^2=3x-2\).

  3. Find the real root of \(3x^3+4x+10=0\).

  4. Find the real root of \(x^3+2x^2=-4x-11\).

  5. Given that \(3x+\frac{2}{x}=7\):

    1. (a) show that \(3x^2 - 7x + 2=0\);
    2. (b) hence find the possible values of x.

In context

  1. A fish tank is a cuboid. Its height is x dm, its width is \((x+2)\) dm and its length is \((x+5)\) dm. Its volume is 150 dm³.

    1. (a) Show that \(x^3 + 7x^2 + 10x - 150=0\).
    2. (b) Find the value of x.

  2. A cyclist rides 120 km at a steady speed of v km/h. A second cyclist rides the same 120 km at \((v+6)\) km/h and takes 1 hour less, so \(\frac{120}{v}-\frac{120}{v+6}=1\).

    1. (a) Show that \(v^2+6v-720=0\).
    2. (b) Find the speed of the slower cyclist.

Stretch

  1. Given that \(3x-\frac{2}{x+2}=5\):

    1. (a) show that \(3x^2 + x - 12=0\);
    2. (b) hence find the possible values of x.

  2. The number of followers of a social media account, in thousands, is modelled by \(N=t^3-6t^2+15t\), where t is the time in months after the account opens. Find when the account first reaches 60 thousand followers.

jmaths.xyz · AI HL · 12.4.3 Polynomial equations with the solver