If 2a 3b 6c 0 then at least one root of the equation ax2 bx c 0 lies in the interval ........

If 2a+3b+6c = 0, then at least one root of the equation ax² +bx + c=0 lies in the interval

(0,1)

(1,2)

(2,3)

None of these

- Given: \(2a + 3b + 6c = 0\).

- Consider the quadratic equation \(ax^2 + bx + c = 0\).

- Using Vieta's formulas, the sum of the roots is \(-b/a\) and the product is \(c/a\).

- Substitute values in \(f(1) = a(1)^2 + b(1) + c = a + b + c\).

- From the given equation, \(2a + 3b + 6c = 0\), solve for \(a+b+c = -2(c)\).

- If \(2a + 3b + 6c = 0\), then \(ax^2 + bx + c=0\) implies \(f(0)+f(1)=0\) hence, At least one root in (0,1).

- Option 1: (0,1)

- Option 2: (1,2)

- Option 3: (2,3)

- Option 4: None of these

Submit Error