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enter image description here Hi, I am not getting how to take "a" as negative root and "b" as positive root, while I am only having X in my quadratic equation. What is the connection of a and b with this quadratic equation in this question?

My approach to this question: I solved it and taken out two roots as -6 and +1, now I am getting confused as I am not having any a and b in a quadratic equation.

Sumaira Rounaq
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    What is it that you're stuck with, exactly? Do you know how to solve the quadratic equation? – Matti P. May 14 '18 at 10:05
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    You don't really need to find the roots of this equation to find the value of the expression. Just simplify until you get an expression entirely in sum of roots and product of roots. – Jasmine May 14 '18 at 10:31
  • Actually I was confused how to take "a" as negative and "b" as positive, because I was getting (x -1)(x+6). Now I got it and solved it. Thank you so much. – Sumaira Rounaq May 15 '18 at 11:46

2 Answers2

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It factors as $(x-1)(x+6)$ so the positive root is $1$ and the negative root is $-6.$ Plug these into your expression(s).

coffeemath
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Hint: The expression reduces to $$ \frac{a}{b}+\frac{b}{a} = \frac{a^2+b^2}{ab} = \frac{(a+b)^2-2ab}{ab} $$ and you know $a+b$ and $ab$ from the coefficients of $x^2+5x-6=0$.

The talk about positive and negative roots is a red herring because the original expression is symmetric in $a$ and $b$, even though it does not look symmetric.

lhf
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