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Algebra Level 4

If m , n m,n be roots of quadratic equation a x 2 + b x + c = 0 ax^2+bx+c =0 ,then roots of the equation ( 4 a + 2 b + c ) x 2 + ( 4 a − b − 2 c ) x + ( a − b + c ) = 0 (4a+2b+c)x^2+(4a-b-2c)x+(a-b+c) = 0 can be expressed as m + e m + f , n + g n + h \dfrac{m+e}{m+f} , \dfrac{n+g}{n+h} . Find the value of the product e f g h efgh .


The answer is 4.

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Aakash Khandelwal by Aakash Khandelwal , 21, India

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2 solutions

Rajen Kapur
Oct 16, 2015

Divide out the second equation by a, and put b a = − m − n \dfrac {b}{a}= -m - n and c a = m n \dfrac{c}{a} = mn . Then factorize to get m + 1 m − 2 , n + 1 n − 2 \dfrac{m+1}{m - 2},\dfrac{n + 1}{n - 2} as the roots. Thus efgh = 4.

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Aakash Khandelwal
Oct 16, 2015

Use transformation of roots

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very precise solution

Utkarsh Grover - 5 years, 8 months ago

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