Multiple choice

If a, b, c be the $4th$, $7th$ and $10th$ term of an AP respectively then the sum of the roots of the equation $ax^2-2bx+c=0$

  1. $-\displaystyle\frac{b}{a}$
  2. $-\displaystyle\frac{2b}{a}$
  3. $\displaystyle\frac{c+a}{a}$

  4. Cannot be determined unless some more information is given about the AP.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In an AP, a = a1 + 3d, b = a1 + 6d, c = a1 + 9d. The equation is (a1+3d)x^2 - 2(a1+6d)x + (a1+9d) = 0. Sum of roots = -(-2b)/a = 2b/a. However, checking the options, (c+a)/a = (2a1+12d)/(a1+3d) = 2(a1+6d)/(a1+3d) = 2b/a. Thus, (c+a)/a is equivalent to 2b/a.

Keep practicing — related questions