Assertion :If $(a^{2} - 4) x^{2} + (a^{2} - 3 a + 2) x + (a^{2} - 7 a + 10) = 0$ is an identity, then the value of $a$ is $2$ . Reason: If $a - b = 0$ , then $a x^{2} + b x + c = 0$ is an identity.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

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Assertion is correct but Reason is incorrect.

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Assertion is incorrect but Reason is correct.

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Solution

The correct option is C Assertion is correct but Reason is incorrect.
An equation is an identity if it is true for any value of variable.
For Assertion :
If $a = 2$ ,
$(a^{2} - 4) x^{2} + (a^{2} - 3 a + 2) x + (a^{2} - 7 a + 10)$
$= (2^{2} - 4) x^{2} + (2^{2} - 3 \times 2 + 2) x + (2^{2} - 7 \times 2 + 10)$
$= (4 - 4) x^{2} + (6 - 6) x + 14 - 14 = 0$
Then, the equation will always satisfy no matter what is the value of $x$ . So, this is an identity.
For Reason:
For $a - b = 0$ , the equation $a x^{2} + b x + c = 0$ does not becomes an identity.
Hence, option 'C' is correct.

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Assertion :If (a2−4)x2+(a2−3a+2)x+(a2−7a+10)=0 is an identity, then the value of a is 2. Reason: If a−b=0, then ax2+bx+c=0 is an identity.

Assertion :If $(a^{2} - 4) x^{2} + (a^{2} - 3 a + 2) x + (a^{2} - 7 a + 10) = 0$ is an identity, then the value of $a$ is $2$ . Reason: If $a - b = 0$ , then $a x^{2} + b x + c = 0$ is an identity.