Question

What two numbers multiply to 15 and add to 6

Answer 1

Answer:

$\left ( \frac{6+\sqrt{24}i}{2}\,,\,\frac{6- \sqrt{24}i}{2} \right )\,,\,\left (\frac{6-\sqrt{24}i}{2}\,,\,\frac{6+ \sqrt{24}i}{2} \right )$

Step-by-step 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 $Ax^2+Bx+C=0$ , $x=\frac{-B\pm \sqrt{B^2-4AC}}{2A}$

Solving  $a^2-6a+15=0$ :

$a=\frac{6\pm \sqrt{36-60}}{2}=\frac{6\pm \sqrt{24}i}{2}$

For $a=\frac{6+\sqrt{24}i}{2}$ , $b=6-\frac{6+ \sqrt{24}i}{2}=\frac{12-6-\sqrt{24}i}{2}=\frac{6- \sqrt{24}i}{2}$

For $a=\frac{6-\sqrt{24}i}{2}$ , $b=6-\frac{6- \sqrt{24}i}{2}=\frac{12-6+\sqrt{24}i}{2}=\frac{6+ \sqrt{24}i}{2}$

Answer 2

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