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Find the value of a if x^3-3x+a=0 has th...

Find the value of `a` if `x^3-3x+a=0` has three distinct real roots.

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The correct Answer is:
Real and distinct roots if `a in(-2,2)`
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Find the value of k if x^(3)-3x+a=0 has three real distinct roots.

The real number k for which the equation 2x^3 + 3x +k=0 has two distinct real roots in [0, 1]

Knowledge Check

  • Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0 and qgt0 . Then which one of the following holds?

    A
    The cubic has maxima at both `sqrt(p/3)` and `-sqrt(p/3)`
    B
    The cubic has minima at `sqrt(p/3)` and maxima at `-sqrt(p/3)`
    C
    The cubic has minima st `-sqrt(p/3)` and maxima at `sqrt(p/3)`
    D
    The cubic has minima at both `sqrt(p/3)` and `-sqrt(p/3)`

  • The set of all positive real values of k, for which the equation x^(3) - 9x^(2) + 24x - k = 0 has three distinct real roots, is the interval :

    A
    (18, 21)
    B
    (16,20)
    C
    (14,18)
    D
    12, 16)

  • Find the real a if the equation x^3-3x^2+ax-1=0 has three positive soluation, then

    A
    `4`
    B
    `1/3`
    C
    `-1/3`
    D
    `3`

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    Find the values of k for which the equation x^(2)-4x+k=0 has distinct real roots.

    Find a for which x^(2)+(a-b)x+(1-a-b)= has two distinct real roots for AA b in R

    If the equation 2x^(3) -6x + k=0 has three real and distinct roots, then find the value (s) of k.

    Find the values of k for which the given equation has real roots: 9x^(2)+3kx+4=0

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