Solving Polynomial Equations (AQA A-Level Further Maths): Quizzes

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Solving Polynomial Equations
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What type of solutions result when the discriminant (b24ac)(b^2 - 4ac) is negative?

Imaginary solutions

If z=a+biz = a + bi solves a polynomial with real coefficients, what else must be a solution?

z=abiz^* = a - bi

Why must a cubic equation with real coefficients have at least one real root?

Complex roots come in pairs

For complex number z=a+biz = a + bi, what is zzzz^* always equal to?

A real number

For complex number z=a+biz = a + bi, what is z+zz + z^* always equal to?

A real number

If 3+4i3 + 4i is a root of a quadratic with real coefficients, what is the other root?

34i3 - 4i

How do complex roots appear in polynomial equations with real coefficients?

In conjugate pairs

A polynomial with real coefficients always has how many complex solutions?

An even number

For quadratic with roots α\alpha and β\beta, what is the equation?

x2(α+β)x+αβ=0x^2 - (\alpha + \beta)x + \alpha\beta = 0

If 25i2 - 5i is a root of a quartic with real coefficients, what else must be a root?

2+5i2 + 5i

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