Quadratic EquationHard
Question
If 2a + 3b + 6c = 0 (a,b,c ∈ R) then the quadratic equation ax2 + bx + c = 0 has
Options
A.at least one root in [0, 1]
B.at least one root in [2, 3]
C.at least one root in [4, 5]
D.none of these
Solution
Let f(x) = 
+ cx ⇒ f(0) = 0 and f(1) = 
+ c = 
Also f(x) is continuous and differentiable in [0,1] and [0, 1[. So by Rolle’s theorem, f′(x) = 0 .
i.e. ax2 + bx + c = 0 has at least one root in [0, 1]
+ cx ⇒ f(0) = 0 and f(1) = + c = Also f(x) is continuous and differentiable in [0,1] and [0, 1[. So by Rolle’s theorem, f′(x) = 0 .
i.e. ax2 + bx + c = 0 has at least one root in [0, 1]
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