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Solved: Consider the equation mx^2 - (m + 3)x + 2m + 9 = 0, where m ∈ ℝ.... [IB Mathematics Analysis and Approaches (AA)] | RevisionDojo

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Question

HLPaper 2

Consider the equation $mx^2 - (m + 3)x + 2m + 9 = 0$ , where $m ∈ ℝ$ .

Write down an expression for the product of the roots, in terms of $m$ .

[1]

Verified

Solution

product of roots $=\frac{2m+9}{m}$ A1

Hence or otherwise, determine the values of m such that the equation has one positive and one negative real root.

[3]

Verified

Solution

recognition that the product of the roots will be negative M1 $\frac{2m+9}{m}<0$ A1 critical values $m=0,-\frac{9}{2}$ seen A1 $-\frac{9}{2}<m<0$ A1

Find for what values there is one distinct real root.

[3]

Verified

Solution

Setting discriminant to 0

$\Delta = b^2-4ac$
$(m+3)^2-4m(2m+9)=0$

Solving for $m$

$m^2+6m+9-8m^2-36m=-7m^2-30m+9=0$
$m=\frac{30\pm\sqrt{900+252}}{-14}$
$m\approx-4.57$ or $0.28$

Mathematics Analysis and Approaches (AA) International Baccalaureate (IB) Practice Question: Consider the equation mx^2 - (m + 3)x + 2m + 9 = 0, where m ∈ ℝ. 1. Write down an expression for the product of the roo...