An algebra problem by fred fan
x^2 - 7x + 12=0
Find the sum for all values of x
The answer is 7.
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2 solutions
That's awesome. +1 for teaching me something new!
To those who are wondering how is it possible -
Roots of any equation of form a x 2 + b + c = 0 are
2 a − b + b 2 − 4 a c , 2 a − b − b 2 − 4 a c
On adding them, we get
= 2 a − b + b 2 − 4 a c + 2 a − b − b 2 − 4 a c = 2 a − b + b 2 − 4 a c − b − b 2 − 4 a c = 2 a − 2 b = a − b
In fact, if you apply the same logic, you get the product of roots of an equation as a c
The roots of the quadratic equation comes out to be
x=3 or x=4
hence the sum of all values of x=7
Moderator note:
There's an immediate solution. Can you find it?
@Challenge Master, @Calvin Lin Sir, The immediate Solution is Vieta's :)
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Yes mehul you are absolutely right.
Upvote if you are satisfied
Sum of roots of a x 2 + b x + c = 0 is a − b
So sum of roots of x 2 − 7 x + 1 2 is 1 − ( − 7 ) = 7