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(A) The given quadratic equation is $x^2 - 2ax + (a^2 - 4) = 0$.We can rewrite this as $x^2 - 2ax + (a-2)(a+2) = 0$.Factoring the quadratic equation,w

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(A) The given quadratic equation is $x^2 - 2ax + (a^2 - 4) = 0$.We can rewrite this as $x^2 - 2ax + (a-2)(a+2) = 0$.Factoring the quadratic equation,we get $(x - (a-2))(x - (a+2)) = 0$.Thus,the roots are $x_1 = a-2$ and $x_2 = a+2$.Since $a-2 We are given the conditions: $a-2  6$.From $a-2 From $a+2 > 6$,we get $a > 4$.Since there is no value of $a$ that satisfies both $a  4$ simultaneously,the number of integral values of $a$ is $0$.

Number of integral values of $a$ for which the smaller root of the quadratic equation $x^2 - 2ax - 4 + a^2 = 0$ is smaller than $1$ and the larger root is greater than $6$ is

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