Graphs of two quadratic expressions y=f1(x) and y=f2(x) are shown in figure. Which of the following statement(s) is/are true?

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Graphs of two quadratic expressions $y = f_{1} (x) a n d y = f_{2} (x)$ are shown in figure. Which of the following statement(s) is/are true?

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The equation $f_{1} (x) . f_{2} (x) = 0$ has 2 distinct roots

Sum of roots of $f_{1} (x) = 0$ is greater than sum of roots of $f_{2} (x) = 0$

Both roots of $f_{1} (x) = 0 a n d f_{2} (x) = 0$ are common

Sum of roots of $f_{1} (x) = 0$ is less than sum of roots of $f_{2} (x) = 0$

answer is A, D.

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Detailed Solution

The roots of $y = f_{1} (x)$ are $α, α$ whereas the roots of $y = f_{2} (x)$ are $α, β$ where $β < α$

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