Question

Which of the following statements regarding quadratic equations are true?

(A) Solution set for the equation is 6x² - 5x = 4 is \(\left( {\frac{{ - 1}}{2},\frac{4}{3}} \right)\)

(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 is 3 times the other, then K = 27/256

1. (A),(B) and (C)
2. (A) and (B) only
3. (B) and (C) only
4. (C) and (A) only

Answer 1

Correct Answer - Option 2 : (A) and (B) only

CALCULATION:

In questions like this, always follow logical deduction and always go by the options.

In statement (A), substituting both the values, we find that they satisfy the equation.

∴ Option (3) can be neglected.

In statement (B), solving the equations, we find out that the roots are equal to -1/3.

In statement (C) after putting 27/256 in place of K, we find out that one of the roots is equal to 0.71(approx) whereas the other is about 0.03(approx) which does not satisfy the criteria.

Always try to solve them by the options provided.