The roots of the equation x² − px + 12 = 0 are in the ratio 1 : 3. Find the value of p (p 0).

Question

The roots of the equation x² − px + 12 = 0 are in the ratio 1 : 3. Find the value of p (p > 0).

Accepted Answer

8. Let the roots be a and 3a. Product = 3a² = 12, so a² = 4 and a = 2. Sum of roots = 4a = p = 8. (Roots 2 and 6 check: product 12, sum 8.)

The roots of the equation $x^{2} - p x + 12 = 0$ are in the ratio 1 : 3. Find the value of $p (p > 0)$ .