Question

If the roots of the quadratic equation \( x^2 - 35x + c = 0 \) are in the ratio 2:3 and \( c = 6K \), then \( K \) is:

• A. \( 49 \)
• B. \( 14 \)
• C. \( 21 \)
• D. \( 7 \)

Hint:

When given a ratio of roots, express them in terms of a variable and use sum and product of roots to solve.

Answer 1

The Correct Option is A

Step 1: Express Roots in Terms of a Variable Let the roots be \( 2x \) and \( 3x \). Step 2: Use Sum and Product of Roots Sum of roots: \[ 2x + 3x = 35 \Rightarrow 5x = 35 \Rightarrow x = 7 \] Product of roots: \[ (2x)(3x) = c \Rightarrow 6x^2 = c \] Substituting \( x = 7 \): \[ c = 6(7^2) = 6(49) = 294 \] Since \( c = 6K \), \[ 6K = 294 \Rightarrow K = 49 \] Thus, the correct answer is 49.