Multiple choice

If the roots of the equation $(a-2b+c)x^2+(b+a-2c)x+(b+c-2a)=0$ be equal then which of the following is true

  1. $a=2b$
  2. $a=b$
  3. $a=2c$
  4. $a=b=c$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac = 0. Here A = (a-2b+c), B = (b+a-2c), C = (b+c-2a). Note that A+B+C = 0. If A+B+C = 0, then one root is 1. If roots are equal, both roots are 1. Product of roots C/A = 1, so C=A. (b+c-2a) = (a-2b+c) => b-2a = a-2b => 3b = 3a => a=b.

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