Respuesta :
You can find what c is by completing the square.
y = x² - 11x + [tex] \frac{121}{4} [/tex] and this simplifies to (x - [tex] \frac{11}{2} [/tex])²
So, c is [tex] \frac{121}{4} [/tex]
y = x² - 11x + [tex] \frac{121}{4} [/tex] and this simplifies to (x - [tex] \frac{11}{2} [/tex])²
So, c is [tex] \frac{121}{4} [/tex]
Answer:
The value of c is [tex]\frac{121}{4}[/tex]
Step-by-step explanation:
A perfect square trinomial is trinomial that can be written as the square of a binomial.
If, [tex]x^2-11x+c[/tex] is a perfect square trinomial,
Then, we can write,
[tex]x^2-11x+c=(x+a)^2[/tex] ---------(1)
Where a is any real number,
[tex]x^2-11x+c=x^2+2ax+a^2[/tex]-------(2)
By comparing the coefficient of x,
We get,
[tex]2ax = -11[/tex]
[tex]\implies a = -\frac{11}{2}[/tex]
By substitution the value of a in equation (2),
[tex]x^2-11x+c=x^2+2\times -\frac{11}{2}x+(-\frac{11}{2})^2[/tex]
[tex]\implies x^2-11x+c=x^2-11x+\frac{121}{4}[/tex]
Again by comparing,
[tex]c=\frac{121}{4}[/tex]
Hence, The value of c is [tex]\frac{121}{4}[/tex]
