Solve quartic as quadratic

A question is this type if and only if it involves solving x⁴ + bx² + c = 0 by treating it as a quadratic in x².

6 questions · Moderate -0.2

1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown
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Pre-U Pre-U 9794/2 2016 Specimen Q4
7 marks Moderate -0.3
4
  1. Show that \(2 x ^ { 2 } - 10 x - 3\) may be expressed in the form \(a ( x + b ) ^ { 2 } + c\) where \(a , b\) and \(c\) are real numbers to be found. Hence write down the co-ordinates of the minimum point on the curve.
  2. Solve the equation \(4 x ^ { 4 } - 13 x ^ { 2 } + 9 = 0\).
Pre-U Pre-U 9794/2 2019 Specimen Q4
7 marks Moderate -0.3
4
  1. Show that \(2 x ^ { 2 } - 10 x - 3\) may be expressed in the form \(a ( x + b ) ^ { 2 } + c\) where \(a , b\) and \(c\) are real numbers to be found. Hence write down the coordinates of the minimum point on the curve.
  2. Solve the equation \(4 x ^ { 4 } - 13 x ^ { 2 } + 9 = 0\).
CAIE P1 2011 November Q3
5 marks Moderate -0.8
\includegraphics{figure_3} The diagram shows the curve \(y = 2x^5 + 3x^3\) and the line \(y = 2x\) intersecting at points \(A\), \(O\) and \(B\).
  1. Show that the \(x\)-coordinates of \(A\) and \(B\) satisfy the equation \(2x^4 + 3x^2 - 2 = 0\). [2]
  2. Solve the equation \(2x^4 + 3x^2 - 2 = 0\) and hence find the coordinates of \(A\) and \(B\), giving your answers in an exact form. [3]
OCR C1 2014 June Q3
5 marks Standard +0.3
Find the real roots of the equation \(4x^4 + 3x^2 - 1 = 0\). [5]
OCR MEI C1 2009 June Q10
4 marks Moderate -0.3
Find the real roots of the equation \(x^4 - 5x^2 - 36 = 0\) by considering it as a quadratic equation in \(x^2\). [4]
Edexcel C1 Q1
3 marks Standard +0.3
Find in exact form the real solutions of the equation $$x^4 = 5x^2 + 14.$$ [3]