Question

If 7x2 + 35x +42 = 7(x + a)(x +B), then a + b = (1) 2 (2) 3 > (3) 4 (4) None of these​

Answer 1

Answer:

{(1, 3) (1, 4) (1, 5) (1, 6) (2, 3) (2, 4) (2, 5) (2, 6) (3,3) (3, 4) (3,5) (3, 6)}

If A = {1 , 2 , 3} ,  B = {3 , 4 , 5} ,  C = {4 ,

Step-by-step explanation:

{(1, 3) (1, 4) (1, 5) (1, 6) (2, 3) (2, 4) (2, 5) (2, 6) (3,3) (3, 4) (3,5) (3, 6)}

If A = {1 , 2 , 3} ,  B = {3 , 4 , 5} ,  C = {4 , 6}

then, to find A X (B U C)

B U C = combination of unique elements of set B and C.

B U C = {3, 4 , 5, 6}

Using associative property of set:

A X (B U C) = (A X B ) U ( A X  C)

To find cartesian products:

(i) A X B = {1 , 2 , 3 } X {3 , 4 , 5}

             = {(1 , 3), (1 , 4), (1 , 5), (2 , 3), (2 , 4), (2 , 5), (3 , 3), (3 , 4), (3 , 5)}

(i) A X C = {1 , 2 , 3 } X {4 , 6}

             = {(1 , 4), (1 , 6), (2 , 4), (2 , 6), (3 , 4), (3 , 6)}

(A X B ) U ( A X  C) = {(1 , 3), (1 , 4), (1 , 5), (2 , 3), (2 , 4), (2 , 5), (3 , 3), (3 , 4), (3 , 5)} U {(1 , 4), (1 , 6), (2 , 4), (2 , 6), (3 , 4), (3 , 6)}

      Ans         = {(1 , 3), (1 , 4), (1 , 5), (1 , 6), (2 , 3), (2 , 4), (2 , 5), (2 , 6), (3 , 3), (3 , 4), (3 , 5), (3 , 6)}

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