CBSE Class 9 Answered
What must be added to x^4+6x^3+19x^2+30x to make it a perfect square?
Asked by ddastez | 04 Jun, 2014, 09:00: PM
Expert Answer
Let:
(ax^2 + bx + c)^2 = x^4 + 6x^3 + 19x^2 + 30x + c^2.
We have:
(ax^2 + bx + c)^2 = (a^2)x^4 + (2ab)x^3 + (2ac + b^2)x^2 + (2bc)x + c^2
Comparing x^4 terms ==> a^2 = 1 ==> a = 1 (pick positive value for simplicity)
Comparing x^3 terms ==> 2ab = 6 ==> 2b = 6 ==> b = 3
Comparing x terms ==> 2bc = 30 ==> 6c = 30 ==> c = 5.
Since the term needed to be added to make it a perfect square is c^2, we need to add 5^2 = 25 on both sides
(ax^2 + bx + c)^2 = x^4 + 6x^3 + 19x^2 + 30x + c^2.
We have:
(ax^2 + bx + c)^2 = (a^2)x^4 + (2ab)x^3 + (2ac + b^2)x^2 + (2bc)x + c^2
Comparing x^4 terms ==> a^2 = 1 ==> a = 1 (pick positive value for simplicity)
Comparing x^3 terms ==> 2ab = 6 ==> 2b = 6 ==> b = 3
Comparing x terms ==> 2bc = 30 ==> 6c = 30 ==> c = 5.
Since the term needed to be added to make it a perfect square is c^2, we need to add 5^2 = 25 on both sides
Answered by Dharma Teja | 05 Jun, 2014, 11:21: AM
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