JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

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Analyzing +4 | -1

If a,b,c are real numbers such that a + b + c = 0, then the
quadratic equation

3a{x^2} + 2bx + c = 0

has:

View answer and explanation

Correct option: A

At least one root in [0, 1]

Option A (At least one root in [0, 1]) is correct because applying Rolle's theorem to the function

f(x) = ax^3 + bx^2 + cx

on the interval [0, 1] shows that there must be at least one root of

3ax^2 + 2bx + c = 0

in the interval [0, 1].

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