﻿ If a, b, c Ïµ R and a + b + c = 0, then the quadratic equation 3 ax2 + 3ax2 + 2bx + c = 0 has : Kaysons Education

# If a, b, c Ïµ R and a + b + c = 0, Then The Quadratic Equation 3 ax2 + 3ax2 + 2bx + c = 0 Has

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## Question

### Solution

Correct option is

At least one root in [0, 1]

Let f (x) = ax3 + bx2 + cx. Note that f is continuous and derivable on R. also f (0) = 0 and f (1) = a + b + c = 0. By the rolle’s therem, there exists at least one α Ïµ (0, 1) such that

Thus, 3ax2 + 2bx + c = 0 has at least one root in [0, 1].

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