2021 · Q31
If one of the roots of the equation ax² − 4ax + 15 = 0 is 3/2, then what is the sum of the squares of the roots ?
Elementary MathematicsAlgebra
- A15/2
- B17/2
- C19/2
- D21/2
Explanation
Substituting x = 3/2: a(9/4) − 4a(3/2) + 15 = 0 gives −15a/4 + 15 = 0, so a = 4. For ax² − 4ax + 15 = 0, the sum of roots is 4 and the product is 15/a = 15/4. The sum of the squares is (sum)² − 2(product) = 16 − 15/2 = 17/2. This is option (b).