Question
Determine what c-value will create a perfect square trinomial for the following expression: \( x^{2}-2 x+c \)
Ask by Jimenez Lowe. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
c = 1
Solution
To determine the value of c that will make x² - 2x + c a perfect square trinomial, we can complete the square. The general form of a perfect square trinomial is (x - a)², which expands to:
(x - a)² = x² - 2ax + a²
In our expression x² - 2x + c, notice the coefficient of x is -2. Setting -2a = -2 gives a = 1. Then a² = 1² = 1.
Thus, c must equal 1 for the expression to become:
x² - 2x + 1 = (x - 1)²
So the value of c is 1.
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Simplify this solution Mind Expander
To create a perfect square trinomial from the expression \( x^{2}-2x+c \), we can complete the square. The coefficient of \( x \) is \(-2\). We take half of this coefficient, which is \(-1\), and then square it, giving us \( (-1)^2 = 1 \). Therefore, the c-value that will create a perfect square trinomial is \( c = 1 \), transforming the expression into \( (x - 1)^2 \). Now you're all set to impress with your quadratic skills! Remember: a perfect square trinomial not only simplifies your life but also helps you factor expressions effortlessly. Practice makes perfect, so try other coefficients and see what c-values emerge!
