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

Answer to Problem 6CYU
The value of c=25 and perfect square is (x-5)2 .
Explanation of Solution
Given:
x2-10x+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:
x2-10x+c .
To make the trinomial a perfect square, find the value of c .
First Find the half of the coefficient of second term:
-102=-5 .
Square the result of the half of the coefficient of the second term will be the c :
c=25 .
The trinomial x2-10x+25 can be written as:
⇒x2-2(x)(5)+(5)2-(5)2+25 .
⇒(x-5)2 .
Hence the value of c=25 and perfect square is (x-5)2 .
(x-3)2+9=0 .
(x-3)2=−9 .
(x-3)=±√−9 .
(x-3)=±3i
x=3i+3 and x=-3i+3 .
Chapter 5 Solutions
Algebra 2
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