What is the sum of the roots of the equation x^2-11x+10=0? 1. 11 2. 7 3. 10 4. -7

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Answer 1 · 2018-05-07T20:45:58

#S=11#

For a quadratic equation of the type

#ax^2+bx+c=0#

We know that the solutions are:

#x_1=(-b+sqrt(Delta))/(2a)#
#x_2=(-b-sqrt(Delta))/(2a)#

We seek to find #S=x_1+x_2#.
By substituting the formulae into this relation, we get:

#S=color(red)((-b+sqrt(Delta))/(2a))+color(red)((-b-sqrt(Delta))/(2a)#

As you can see, the square roots of #Delta# cancel each other.

#=> S = (-2b)/(2a)=-b/a#

In our case, we have

#x^2-11x+10=0#

#a=1#, #b=-11#, #c=10#.

Thus, we must have #color(red)(S=-(-11)/1=11#.

On a related note, you can also prove that #P=x_1x_2=c/a#.

This, together with our sum formula, are called #color(blue)("Viète's relations")#.