Question

Find the value of c that makes x^2–6x + c a perfect square trinomial and write as a binomial squared.

Answer 1

Answer: 9

Step-by-step explanation:

Given

The function is $x^2-6x+c$

To make it a perfect square, compare it with $(a-b)^2=a^2+b^2-2ab$

Here,

$x=a,\\-6x=-2ab\\\\\therefore b=3$

So, c must be square of b i.e. 9

$x^2-6x+c\Rightarrow x^2-6x+9\\\Rightarrow (x-3)^2$

Therefore, value of c is 9.