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Algebra Level 3

If one root of the equation (x-1)(7-x)=m is three times the other, then m equals to

-5 9 -7 5 -9 7 -5/7 0

1 solution

Omkar Kulkarni
Feb 1, 2015

Let one root be $\alpha$ . Hence the other one is $3\alpha$ .

Now, $(x-1)(7-x)=m \Rightarrow x^{2} - 8x + 7 + m = 0$

Hence the sum of the roots is $8$ .

$\alpha + 3\alpha = 8 \Rightarrow \alpha = 4$

And the product of the roots is $7+m$ .

$(\alpha)(3\alpha)=7+m \Rightarrow \boxed{m=5}$

there's something wrong in your calculation. a should be 2, not 4

Edi Nugroho - 6 years, 3 months ago