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Question

$$x^{2} + 5x - (a^{2} + a - 6) = 0$$.


Solution

formula for roots of quadratic  
expression $$ ax^{2}+bx+c = 0 $$ is 
$$ = \dfrac{-b\pm \sqrt{b^{2}-4ac}}{2a} $$
So for $$ x^{2}+5x-(a^{2}+a-6) = $$
$$ \Rightarrow \dfrac{-5\pm \sqrt{25+4(a^{2}+a-6)}}{2} $$
$$ \Rightarrow \dfrac{-5\pm \sqrt{4a^{2}+4a+1}}{2} $$
$$ \Rightarrow \dfrac{-5}{2}\pm \sqrt{(a+1/2)^{2}} $$
$$ = \dfrac{-5}{2}\pm (a+1/2) $$ 

1124786_1143337_ans_0f4ff03a89d24008af02d70196fc1305.jpg

Mathematics

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