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What number should be added to the expression x2 + 4x to change it into a perfect square trinomial?
Solution:
A perfect square trinomial is defined as an algebraic expression that is obtained by
squaring a binomial expression.
Given, the expression is x2 + 4x + C -------- (1)
A perfect square is an expression in the form (x+a)² which can be written in a trinomial form as
(x + a)2 = (x + a)(x + a) = x2 + ax + ax + a2
(x+a)2 = x2 + 2ax + a2 -------------------------- (2)
Comparing (1) and (2)
2a = 4
a = 2
Also, a2 = C
C = (2)2 = 4
Therefore, the number that should be added is 4.
Aliter:
A function that can be obtained by squaring the binomial expression is a perfect square trinomial. It satisfies the condition b2 - 4ac = 0 and are in the form of ax2 + bx + c.
As per the question, b = coefficient of x, a = coefficient of x2 and c = constant term.
⇒ b2 - 4ac = 0
⇒ b2 = 4ac
⇒ (4)2 = 4 (1) c
⇒ 16 = 4 × c
By dividing both the sides by 4, we get
⇒ c = 4
What number should be added to the expression x2 + 4x to change it into a perfect square trinomial?
Summary:
The number that should be added to the expression x2+4x to change it into a perfect square trinomial is 4.
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