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help with a further maths question

hey,

how would i solve 5(iii)? i’ve seemed to figure out i and ii but can’t get my head around iii.

many thanks.

One root of the quadratic equation x^2 + ax + b = 0, where an and b are real, is 16 - 30i.
(i) Write down the other root of the quadratic equation.
(ii) Find the values of a and b.

(iii) Use an algebraic method to solve the quartic equation y^4 + ay^2 + b = 0. (7 marks)
Original post by easten
hey,

how would i solve 5(iii)? i’ve seemed to figure out i and ii but can’t get my head around iii.

many thanks.

One root of the quadratic equation x^2 + ax + b = 0, where an and b are real, is 16 - 30i.
(i) Write down the other root of the quadratic equation.
(ii) Find the values of a and b.

(iii) Use an algebraic method to solve the quartic equation y^4 + ay^2 + b = 0. (7 marks)


The eqn in (iii) is the same as the original but with x=y2x=y^2.

Since you have two solutions x=16±30ix=16\pm 30i then that means y2=16±30iy^2 = 16\pm 30i ... now square roots of these two possibilities.

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