Question

is :
Q. Type. My
3a+2 – 3a+1
The value of
4 x 34 – 3a
2+2
za+1
का मान होगा-
x 3a – 3a
PRINCE
0 (A) 0
O (B) 1
(C) 2.
(D) 3​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The value of a for which the below is identity

$\sf{( {a}^{2} - 3a + 2 ) {x}^{2} + ( {a}^{2} - 5a + 6 ) x + ( {a}^{2} - 4 ) = 0}$

(A) 0

(B) 1

(C) 2

(D) 3

CONCEPT TO BE IMPLEMENTED

The expression

$\sf{A {x}^{2} + Bx + C = 0}$

is an identity if A = B = C = 0

EVALUATION

Here it is given that

$\sf{( {a}^{2} - 3a + 2 ) {x}^{2} + ( {a}^{2} - 5a + 6 ) x + ( {a}^{2} - 4 ) = 0}$

Comparing with

$\sf{A {x}^{2} + Bx + C = 0} \: \: \: we \: get$

$\sf{A = ( {a}^{2} - 3a + 2 ) \:, B = ( {a}^{2} - 5a + 6 ) ,\: C = \: ( {a}^{2} - 4 ) }$

So the above is identity when

$\sf{A = 0 \:, B = 0 ,\: C = \: 0 }$

$\sf{ \implies \: ( {a}^{2} - 3a + 2 ) = 0 \:, ( {a}^{2} - 5a + 6 ) = 0 , ( {a}^{2} - 4 ) = 0}$

Now

$\sf{ ( {a}^{2} - 3a + 2 ) = 0 \: \: gives \: \: \: \: a = 1 \:, 2}$

$\sf{ ( {a}^{2} - 5a + 6 ) = 0 \: \: \: gives \: \: a =2 ,3 }$

$\sf{ ( {a}^{2} - 4 ) = 0 \: \: gives \: \: a = - 2, 2 }$

This above together is satisfied by a = 2

FINAL ANSWER

Hence the correct option is (C) 2

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