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Elena L [17]
3 years ago
14

What two numbers multiply to 15 and add to 6

Mathematics
2 answers:
WITCHER [35]3 years ago
8 0

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}

Katen [24]3 years ago
6 0
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
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