Question

If (X+a)(X+b)=X^2-5X-300.Find the values of a^2+b^2.

Answer 1

Hey mate.........

Here is the solution that the question.......

$( {x}^{2} + a)( {x}^{2} + b) = {x}^{2} + x(a + b) + ab \\ \\ \\ \\ {x}^{2} + x(a + b) + ab \: = {x}^{2} - 5x - 300$


$a \: + b = - 5 \\ \\ab = - 300$
${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ {( - 5)}^{2} = {a}^{2} + {b}^{2} - 600 \\ \\ {a}^{2} + {b}^{2} = 625$

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