Roots of Polynomials (AQA A-Level Further Maths): Quizzes

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Roots of Polynomials
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For ax2+bx+c=0ax^2 + bx + c = 0 with roots α\alpha and β\beta, what is α+β\alpha + \beta?

ba-\frac{b}{a}

For ax2+bx+c=0ax^2 + bx + c = 0 with roots α\alpha and β\beta, what is αβ\alpha\beta?

ca\frac{c}{a}

For ax3+bx2+cx+d=0ax^3 + bx^2 + cx + d = 0 with roots α,β,γ\alpha, \beta, \gamma, what is α+β+γ\alpha + \beta + \gamma?

ba-\frac{b}{a}

For ax3+bx2+cx+d=0ax^3 + bx^2 + cx + d = 0 with roots α,β,γ\alpha, \beta, \gamma, what is αβγ\alpha\beta\gamma?

da-\frac{d}{a}

What pattern do the signs follow in root-coefficient relationships?

Alternating: negative, positive, negative

If α+β=5\alpha + \beta = 5 and αβ=6\alpha\beta = 6, what is α2+β2\alpha^2 + \beta^2?

1313

If α+β=4\alpha + \beta = 4 and αβ=3\alpha\beta = 3, what is 1α+1β\frac{1}{\alpha} + \frac{1}{\beta}?

43\frac{4}{3}

In quartic equations, what does Σα\Sigma\alpha represent?

Sum of all roots

To find equation with roots α3,β3\alpha - 3, \beta - 3, what do you substitute for xx?

y+3y + 3

Before applying root-coefficient formulas, what must you check?

Leading coefficient equals 1

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