Question

The ratio of the sum of the roots and the product of the roots of the quadratic equation \(x^2 - 15x + 50 = 0\) is:

• A. \(3:10\)
• B. \(3:25\)
• C. \(3:50\)
• D. \(5:3\)

Hint:

For a monic quadratic \(x^2+bx+c=0\), sum of roots \(= -b\) and product \(= c\) — no solving required.

Answer 1

The Correct Option is A

Step 1: Use Vieta's formulas for \(ax^2+bx+c=0\).
Sum of roots \(= -\dfrac{b}{a}\), product of roots \(=\dfrac{c}{a}\). For \(x^2-15x+50=0\), we have \(a=1, b=-15, c=50\).
Step 2: Compute sum and product.
Sum \(= -\dfrac{-15}{1}=15\), \quad Product \(=\dfrac{50}{1}=50\).
Step 3: Form and simplify the ratio.
\(\text{Sum} : \text{Product} = 15 : 50 = \dfrac{15}{5} : \dfrac{50}{5} = 3 : 10.\)