If the roots of the equation $x^{3} - a x^{2} + b x - c = 0$ are three consecutive integers, then what is the smallest possible value of b?

- (\frac{1}{\sqrt{3}})

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\frac{1}{\sqrt{3}}

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Solution

The correct option is B $- 1$
Option (B) is the correct answer. Check the video for the approach.

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Similar questions

If the roots of the cubic $x^{3} + a x^{2} + b x + c = 0$ are three consecutive positive integers. Then the value of $\frac{a^{2}}{b + 1}$ is equal to __.

Q. If the roots of the equation

x^{2} - b x + c = 0

are two consecutive integers, then what is the value of

b^{2} - 4 c

If roots of the cubic equation $x^{3}$ + a $x^{2}$ + 146x + c = 0 are three consecutive positive integers. Find the sum of the roots.

Q. If the equation

x^{3} - a x^{2} + b x - a = 0

has three real roots then which of the following is true (CAT 2000)

Q. Assertion :If roots of the equation

x^{2} - b x + c = 0

are two consecutive integers, then

b^{2} - 4 c = 1

Reason: If

a, b, c

are odd integer then the roots of the equation

4 a b c x^{2} + (b^{2} - 4 a c) x - b = 0

are real and distinct.

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If the roots of the equation x3−ax2+bx−c=0 are three consecutive integers, then what is the smallest possible value of b?

The correct option is B −1Option (B) is the correct answer. Check the video for the approach.

If the roots of the equation $x^{3} - a x^{2} + b x - c = 0$ are three consecutive integers, then what is the smallest possible value of b?

The correct option is B $- 1$
Option (B) is the correct answer. Check the video for the approach.