Respuesta :
While making a perfect square for the given quadratic equation [tex]\rm x^2+3x+c=\frac{7}{4} +c[/tex] the value of c is 9/4
It is given that the quadratic equation [tex]\rm x^2+3x+c=\frac{7}{4} +c[/tex] while forming the perfect square.
It is required to find the value of c.
What is a quadratic equation?
It is defined as the equation of polynomial of degree two. The standard form of the quadratic equation is as follows:
[tex]\rm ax^2+bx+c=0[/tex] where [tex]\rm a\neq 0[/tex]
We have a quadratic equation:
[tex]\rm x^2+3x+c=\frac{7}{4} +c[/tex]
We know that we can make any quadratic equation into a perfect square by the perfect square trinomial method as follow:
[tex]\rm ax^2+bx+c=0\\\rm ax^2+bx=-c\\\rm ax^2+bx+(\frac{b}{2a})^2 =-c+(\frac{b}{2a})^2\\[/tex]
So, the value of 'c' would be:
[tex]\rm c=(\frac{b}{2a})^2\\[/tex] here b=3 and a=1 by comparing the equation to the standard equation.
[tex]c=(\frac{3}{2\times1} )^2\\c=(\frac{3}{2} )^2\\c=\frac{9}{4}[/tex]
Thus, while making a perfect square for the given equation the value of c is 9/4
Know more about the quadratic equation here:
https://brainly.com/question/2263981
