Edexcel IGCSE Math A 2.7.HB quadratic formula and completing square

Practise the formula-comparison question by matching the denominator and discriminant in the solution form to values in the equation.

Exam points

Use the denominator 2a in the quadratic formula to identify the value of a.
Compare the discriminant expression with the surd form to find the missing constant.

[Maximum number: 3]

Here is a quadratic equation.

ax^2+4x+c=0

The solutions of this equation are given by

x=\frac{-4\pm2\sqrt{39}}{10}

Find the value of a and the value of c.
Show your working clearly.

\begin{gathered} a= \\ c= \end{gathered}

The denominator in the quadratic formula is 2a:
$2a=10\quad\Rightarrow\quad a=5$
The surd part gives:
$b^2-4ac=4\times39$
with b=4 and a=5:
$16-20c=156 \quad\Rightarrow\quad c=-7$

Final answer:
$a=5,\qquad c=-7$

M1 for 2a=10. M1 for using the discriminant correctly. A1 for a=5 and c=-7.

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2.7.HB Quadratic formula and completing the square question 1