Question

What value of b makes the trinomial below a perfect square x^2-bx+100

Answer 1

1. Perfect square trinomials, are 2nd degree polynomials, of the form          $a x^{2} +bx+c$ so that $a \neq 0, b \neq 0, c \neq 0$, which can be written as perfect squares.

2. For example $(x+1) ^{2} = x^{2} +2x+1 (3x-1)^{2}= (3x)^{2}-2(3x)+(-1) ^{2}= 9x^{2}-6x+1$

3. Thus $x^{2} +2x+1, 9x^{2}-6x+1$ are perfect square trinomials.

4. $x^{2} -bx+100= x^{2} -bx+ 10^{2}= (x+10)^{2} or (x-10)^{2}$

5. In the first case -b=20, so b=-20. In the second case, -b=-20, so b=20.

6. b∈{-20, 20}