Question

Which of the following statements regarding quadratic equations are true?
(A) Solution set for the equation 6x²-5x=4 is \(\{-\frac{1}{2},\frac{4}{3}\}\).
(B) The nature of the roots of the equation 9x²+6x+1=0 is equal, real and rational.
(C) If one root of 4x²-3x+K=0 is 3 times the other, then \(K=\frac{27}{256}\)
Choose the correct answer from the options given below:

• A. (A), (B) and (C)
• B. (A) and (B) only
• C. (B) and (C) only
• D. (C) and (A) only

Answer 1

The Correct Option is B

To determine which statements regarding the quadratic equations are true, let's analyze each option one by one.

1. Statement (A): Solution set for the equation \(6x^2 - 5x = 4\) is \(\left\{-\frac{1}{2}, \frac{4}{3}\right\}\). 
2. Statement (B): The nature of the roots of the equation \(9x^2 + 6x + 1 = 0\) is equal, real and rational.
3. Statement (C): If one root of \(4x^2 - 3x + K = 0\) is 3 times the other, then \(K = \frac{27}{256}\).

Therefore, the correct answer is:

(A) and (B) only

.