Consider the following statements : 1. One of the roots of the equation is <strong>ALWAYS</strong> less than 1 if a, b and c are all positive. 2. One of the roots of the equation is <strong>ALWAYS</strong> negative if a, b and c are all negative. Which of the statements given above is/are <strong>CORRECT</strong>?
Consider the following for the next two (02) items that follow : A quadratic equation is given by (a+b+c)x^2-(2a+2b)x+(a+b-c)=0; where a, b and c are real and distinct.
- A. 1 only ✓
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
Correct Answer: A. 1 only
Explanation
Statement 1 is true: if a, b, c \gt 0, then \frac{a+b-c}{a+b+c} \lt 1 because -c \lt c. Statement 2 is false: if a=-2, b=-3, c=-1, the roots are 1 and \frac{-5 - (-1)}{-6} = \frac{2}{3}, neither of which is negative.
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