Quadratic in x^(1/2) - substitution u = √x

Solve equations where substituting u = x^(1/2) (or u = √x) reduces the equation to a standard quadratic in u, e.g. 4x - 11x^(1/2) + 6 = 0, x - 6√x + 4 = 0, 2x - 7x^(1/2) + 3 = 0.

6 questions · Standard +0.2

1.02f Solve quadratic equations: including in a function of unknown

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CAIE P1 2018 November Q1

3 marks Moderate -0.5

1 Showing all necessary working, solve the equation \(4 x - 11 x ^ { \frac { 1 } { 2 } } + 6 = 0\).

Edexcel P1 2019 October Q8

5 marks Standard +0.3

8. Solve, using algebra, the equation $$x - 6 x ^ { \frac { 1 } { 2 } } + 4 = 0$$ Fully simplify your answers, writing them in the form \(a + b \sqrt { c }\), where \(a , b\) and \(c\) are integers to be found.
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OCR C1 2008 June Q4

5 marks Standard +0.3

4 Solve the equation \(2 x - 7 x ^ { \frac { 1 } { 2 } } + 3 = 0\).

OCR C1 2010 January Q5

7 marks Standard +0.3

5 Solve the equation \(x - 8 \sqrt { x } + 13 = 0\), giving your answers in the form \(p \pm q \sqrt { r }\), where \(p , q\) and \(r\) are integers.

OCR C1 2012 June Q7

6 marks Standard +0.3

7 Solve the equation \(x - 6 x ^ { \frac { 1 } { 2 } } + 2 = 0\), giving your answers in the form \(p \pm q \sqrt { r }\), where \(p , q\) and \(r\) are integers.

OCR PURE Q2

4 marks Standard +0.3

2 In this question you must show detailed reasoning. Solve the equation \(3 x + 1 = 4 \sqrt { x }\).