
Concept explainers
To find: the value of c that makes perfect square and write the trinomial as a perfect square.

Answer to Problem 28PPS
The value of c=1214 and perfect square is (x−112)2 .
Explanation of Solution
Given:
x2-11x+c .
Concept used:
An expression obtained from the square of binomial equation is a perfect square trinomial is in the form of ax2+bx+c is said to be a perfect square, if only if it satisfies the condition b2=4ac .
The perfect squares trinomial formula is given as:
(ax)2+2abx+b2=(ax+b)2 .
(ax)2-2abx+b2=(ax-b)2
Calculation:
x2-11x+c .
To make the trinomial a perfect square, find the value of c .
First Find the half of the coefficient of second term:
112 .
Square the result of the half of the coefficient of the second term will be the c :
c=(112)2=1214 .
c=1214 .
The trinomial x2-11x+1214 can be written as:
⇒x2-2(x)(12(11))+(112)2-(112)2+1214 .
⇒(x−112)2 .
Hence the value of c=1214 and perfect square is (x−112)2 .
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