Answer:
[tex]x^2-9x+18=0[/tex]
Step-by-step explanation:
Let us start with the quadratic equation, [tex]ax^2+bx+c=0[/tex]. We know that the sum of the roots is equal to [tex]-\frac{b}{a}[/tex] and the product of them is [tex]\frac{c}{a}[/tex].
Given that the leading coefficient, or a, is 1, let us substitute what we know to find b and c respectively:
SUM OF ROOTS:
[tex]-3+(-6)= -9\\[/tex]
[tex]-\frac{b}{a}=9\\-\frac{b}{1}=9\\-b=9\\b=-9[/tex]
PRODUCT OF ROOTS:
[tex](-3)(-6)=18\\\frac{c}{a}=18\\\frac{c}{1}=18\\c=18[/tex]
Now that we have all three variables, a, b, and c, we can write our quadratic equation:
[tex]x^2-9x+18=0[/tex]
I hope this helps! Let me know if you have any questions :)
