Quadratic question Q3

**yeoky** · June 27th 2009, 11:37 PM

Find the range of values of k if the equation Xsquare+(4K-2)X+(5Ksqure-4)=0 has 2 real and distinct roots of opposite signs.

Thanks.

How do I type X squre in the text box? Thank.

**mr fantastic** · June 27th 2009, 11:39 PM

Originally Posted by yeoky

How do I type X squre in the text box? Thank.

x^2 is the usual convention.

Note: The latex code for $x^2$ is [tex]x^2[/tex]. See here: http://www.mathhelpforum.com/math-he...-tutorial.html

**red_dog** · June 27th 2009, 11:57 PM

The roots are real and distinct $\Rightarrow\Delta>0$

$\Delta=b^2-4ac=4(-k^2-4k+5)$

$k_1=-5, \ k_2=1\Rightarrow k\in(-5,1)$ (1)

The roots are of opposite signs $\Rightarrow x_1x_2<0$

$x_1x_2=5k^2-4<0\Rightarrow k\in\left(-\frac{2}{\sqrt{5}},\frac{2}{\sqrt{5}}\right)$ (2)

From (1) and (2) $\Rightarrow x\in\left(-\frac{2}{\sqrt{5}},\frac{2}{\sqrt{5}}\right)$

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