Math miscellaneousHard
Question
If 2a + 3b + 6c =0, then at least one root of the equation ax2 + bx + c = 0 lies in the interval
Options
A.(0, 1)
B.(1, 2)
C.(2, 3)
D.(1, 3)
Solution
Let f′(x) = ax2 + bx + c ⇒ f(x) = 
+ cx + d
⇒ f(x) =
(2ax3 + 3bx2 + 6cx + 6d), Now f(1) = f(0) = d, then according to Rolle′s theorem
⇒ f′(x) = ax2 + bx + c = 0 has at least one root in (0, 1)
+ cx + d⇒ f(x) =
(2ax3 + 3bx2 + 6cx + 6d), Now f(1) = f(0) = d, then according to Rolle′s theorem ⇒ f′(x) = ax2 + bx + c = 0 has at least one root in (0, 1)
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