Question

What two numbers multiply to 15 and add to 6

Answer 1

Since there are no number that multiply to 155 and add to 6 you must now use the Quadratic Formula.

x=(-b(+/-)√
`b^(2)`-4ac)
2a

Answer 2

`\left ( (6+√(24)i)/(2)\,,\,(6- √(24)i)/(2) \right )\,,\,\left ((6-√(24)i)/(2)\,,\,(6+ √(24)i)/(2)  \right )`

Explanation:

Let a and b be two numbers such that
`a+b=6\,,\,ab=15`

From equation a + b = 6 , we have b = 6 - a . On putting this value of b in equation ab=15 , we get
`a(6-a)=15\Rightarrow 6a-a^2=15\Rightarrow a^2-6a+15=0`

We will solve this equation using quadratic formula : For equation of form
`Ax^2+Bx+C=0` ,
`x=(-B\pm √(B^2-4AC))/(2A)`

Solving
`a^2-6a+15=0` :

`a=(6\pm √(36-60))/(2)=(6\pm √(24)i)/(2)`

For
`a=(6+√(24)i)/(2)` ,
`b=6-(6+ √(24)i)/(2)=(12-6-√(24)i)/(2)=(6- √(24)i)/(2)`

For
`a=(6-√(24)i)/(2)` ,
`b=6-(6- √(24)i)/(2)=(12-6+√(24)i)/(2)=(6+ √(24)i)/(2)`