Finding two numbers given their sum and their product.
I want to know step by step what are the two roots that give you -96 when you add them up and give you -10 when you multiply them.
+18 Just suppose two numbers to be X and Y
Then according to the data given in question
You can say X + Y = -96 ----- (i)
and (X)x(Y) = -10 ----- (ii)
then by using equation (i) X + Y = -96 => X = -96 - Y
Put X = -96 - Y in equation (ii)
(-96 - Y)Y = -10
-96Y - Y2 = -10
Now just simplify the above equation (either by making factors, if possible or just use quadratic formula).
You'll get two values for Y then put them in equation (i) to get values of X
I hope this would help you..
+18 Just suppose two numbers to be X and Y
Then according to the data given in question
You can say X + Y = -96 ----- (i)
and (X)x(Y) = -10 ----- (ii)
then by using equation (i) X + Y = -96 => X = -96 - Y
Put X = -96 - Y in equation (ii)
(-96 - Y)Y = -10
-96Y - Y2 = -10
Now just simplify the above equation (either by making factors, if possible or just use quadratic formula).
You'll get two values for Y then put them in equation (i) to get values of X
I hope this would help you..
+128598 $${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{96}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{10}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{2\,314}}}}{\mathtt{\,-\,}}{\mathtt{48}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{2\,314}}}}{\mathtt{\,-\,}}{\mathtt{48}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{96.104\: \!053\: \!883\: \!222\: \!773\: \!6}}\\
{\mathtt{x}} = {\mathtt{0.104\: \!053\: \!883\: \!222\: \!773\: \!6}}\\
\end{array} \right\}$$
