What two numbers multiply to 15 and add to 6
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:
\(\left ( \frac{6+\sqrt{24}i}{2}\,,\,\frac{6- \sqrt{24}i}{2} \right )\,,\,\left (\frac{6-\sqrt{24}i}{2}\,,\,\frac{6+ \sqrt{24}i}{2} \right )\)
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 \(a=\frac{6-\sqrt{24}i}{2}\) , \(b=6-\frac{6- \sqrt{24}i}{2}=\frac{12-6+\sqrt{24}i}{2}=\frac{6+ \sqrt{24}i}{2}\)