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  • If sum of roots of equation <img alt="\left ( a+1 \right )x^{2}+\left ( 2a+3 \right )x+\left ( 3a+4 \right )= 0" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%20%28%20a&plus;

If sum of roots of equation \left ( a+1 \right )x^{2}+\left ( 2a+3 \right )x+\left ( 3a+4 \right )= 0 is -1, then roots of equation are 

Option: 1

Real & Equal


Option: 2

Real & Distinct


Option: 3

one real & one imaginary


Option: 4

Imaginary


Answers (1)

best_answer

As we learnt in

Sum of Roots in Quadratic Equation

\alpha +\beta = \frac{-b}{a}

 

Now,

\because \: Sum\: =-1\: \Rightarrow \: -\frac{\left ( 2a+3 \right )}{\left (a+1 \right )}=-1\: \Rightarrow \: a=-2

\therefore equation becomes :  -x^{2}-x-2=0

or x^{2}+x+2=0 ;

D=1^{2}-4\left ( 1 \right )\left ( 2 \right )=-7< 0 , so imaginary roots

\therefore Option (D)

Posted by

rishi.raj

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