Multiple choice

If $\displaystyle ^{7}C_{r} + 3 ^{7}C_{r+1} + 3 ^{7}C_{r+2} + ^{7}C_{r+3} > ^{10}C_{4}$, then the quadratic equation whose roots are $\displaystyle \alpha, : \beta$ and $\displaystyle \alpha^{r-1}, : \beta^{r-1}$ have

  1. no common roots

  2. only one common root

  3. two common root

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the binomial identity, the left side becomes C(10, r + 3). The inequality requires C(10, r + 3) > C(10, 4), which gives r = 2. Hence α^(r-1) = α and β^(r-1) = β, so both roots are common.

Keep practicing — related questions