First slide

Theory of equations

Question

If x² +2x +2xy + my - 3 -0 has two rational factors then the values of m will be

Moderate

A

- 6, -2
B

- 6,2
C

6, -2
D

6,2

Solution

Given expression $x^{2} + 2 x + 2 xy + my - 3 = 0$ can be rewritten as
$x^{2} + 2 x (1 + y) + (my - 3) = 0$
But factors are rational ,so discriminant b² - 4ac is a perfect square.
Now, $b^{2} - 4 ac = 4 \{(1 + y)^{2} - (my - 3)\} \geq 0$
$\begin{array}{lrl} \Rightarrow 4 \{y^{2} + 1 + 2 y - my + 3\} \geq 0 \\ \Rightarrow y^{2} + 2 y - my + 4 \geq 0 \end{array}$
Now, taking (-) ve sign, we get m = 6
for +ve sign , we get m=-2

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