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  4. If the product of the roots of the equation x2-3 x+k+5=0 is 7 , then the roots are real for k=

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Q. If the product of the roots of the equation $x^2-3 x+k+5=0$ is 7 , then the roots are real for $k=$

Complex Numbers and Quadratic Equations

Solution:

$ x^2-3 x+k+5=0 $
$\because $ Product of the roots $=7 $
$ \Rightarrow k+5=7 $
$ \therefore k=2 $.
Now for $k =2$, disc $< 0 \Rightarrow$ no real roots