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Solution


Q.

Assertion (A): The roots of equation x² – 7x + 12 = 0 are x = 3 and x = 4.

Reason (R): The splitting of middle term of the equation x² – 7x + 12 = 0 is
(x² – 7/2 x – 7/2 x + 12 = 0).
1 Both A and R are true, and R is the correct explanation of A  
2 Both A and R are true, but R is not the correct explanation of A.
 
3 A is true, but R is false.
 
4 A is false, but R is true.
 

Ans.

(3)

We have, x² – 7x + 12 = 0 ⇒ x² – 4x – 3x + 12 = 0 ⇒ x(x – 4) – 3(x – 4) = 0
⇒ (x – 4)(x – 3) = 0 ⇒ x = 3, 4. ∴ Assertion (A) is true.

In Reason (R): Given, x² – 7x + 12 = x² – (7/2)x – (7/2)x + 12 = 0
This is not middle term splitting because
(–7/2)x × (–7/2)x ≠ 12x²