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The number of values of a for which (a^2...

The number of values of a for which `(a^2-3a+2)x^2+(a^2-5a+6)x+a^2-4=0` is an identity in x is

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The correct Answer is:
` a = 2`
We must have `a^(2) - 3a + 2 = 0`
`rArr a = 1, 2`
and `a^(2) - 5a + 6 = 0 rArr a = 2, 3`
and `a^(2) - 4 = 0 `rArr a = pm 2`
Therefore, when a = 2, the equation will be ture for all real x .
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Knowledge Check

  • The number of values of 'a' for which (a^2-3a+2)x^2+(a^2-5a+6)x+a^2-4 =0 is an identity is

    A
    0
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    A
    `(-infty,-sqrt2pi) cup (sqrt2pi, infty)`
    B
    `-2+pi`
    C
    `(-infty,-sqrt2pi] cup [sqrt2pi, infty)`
    D
    `-2-pi/4`

  • The number of solutions for the equations x^(2) -5 |x| +6 =0 is-

    A
    4
    B
    1
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