(A) The given quadratic equation is $x^2 - 2ax + (a^2 - 4) = 0$.We can factorize this as $(x - (a - 2))(x - (a + 2)) = 0$.Thus,the roots are $x_1 = a

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(A) The given quadratic equation is $x^2 - 2ax + (a^2 - 4) = 0$.We can factorize this as $(x - (a - 2))(x - (a + 2)) = 0$.Thus,the roots are $x_1 = a - 2$ and $x_2 = a + 2$.Since $a - 2 We are given the conditions:$1$) $a - 2 $2$) $a + 2 > 6 \implies a > 4$Combining these,we need $a 4$,which is impossible.Therefore,there are no integral values of $a$ that satisfy these conditions.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Quadratic expressions and Position of roots

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

A
$0$
B
$1$
C
$2$
D
infinite values

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4-2.Quadratic Equations and Inequations

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Quadratic expressions and Position of roots

The set of values of $a$ such that $x^2 - 2ax + a^2 - 6a \leqslant 0$ for all $x \in [1, 2]$ is

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If $ax^2 + bx + c < 0$ for all $x \in R$ and the expressions $cx^2 + ax + b$ and $ax^2 + bx + c$ have their extreme values at the same point $x$,then for the expression $cx^2 + ax + b$:

DifficultAP EAMCET 2025

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The set of all real values of $\lambda$ for which the quadratic equation $(\lambda^{2}+1)x^{2}-4\lambda x+2=0$ has exactly one root in the interval $(0,1)$ is

DifficultJEE MAIN 2020

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

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