Finding m − n m-n

Algebra Level 3

If m m and n n are the roots of x 2 − 10 x + 10 = 0 x^{2}-10x+10=0 , find the value of ( m − n ) ( n − m ) (m-n)(n-m) .


The answer is -60.

Benedict Dimacutac by Benedict Dimacutac , 21, Philippines

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3 solutions

Sanidhya Mathur
Apr 18, 2015

For a quadratic equation ax²+bx+c=0, where m and n are two roots, m+n= - b/a and m.n= c/a

Here a=1 b=-10 and c=10

Here m+n = - (-10)/1 and m.n=10/1

We need (m-n) (n-m) = -(m-n)²

Also (m-n)²= (m+n) ²- 4(m.n) = 100-40 = 60

Hence -(m-n)² = - 60

Thanks.. Keep smiling.. :) :)

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Hey yo,

By completing the square,

you will get 2 roots,

m = 5 + (15)^(0.5),

n = 5 - (15)^(0.5),

Then, (m-n)(n-m) = -60

Thanks....

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Uahbid Dey
Apr 28, 2015

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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