Multiple choice

If $\cfrac { 7 }{ 2 } $ and $1$ are the roots of the equation $\begin{vmatrix} 2x & 3 & 7 \ 2 & 2x & 2 \ 7 & 6 & 2x \end{vmatrix}=0$, then the third root is

  1. $-\cfrac { 7 }{ 2 } $
  2. $-\cfrac { 9 }{ 2 } $
  3. $-\cfrac { 3 }{ 2 } $
  4. $-\cfrac { 5 }{ 2 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The determinant of the 3x3 matrix is a cubic polynomial in x. Given the roots 7/2 and 1, the product of all three roots is determined by the constant term of the polynomial. By expanding the determinant, one can find the sum of roots or use the property that the product of roots equals -d/a.

Keep practicing — related questions