The value of 'c' and 'd' are 9 and 3 respectively in the given equation [tex]\rm\rm x^2+6x+c= (x+d)^2[/tex]
It is given that the quadratic expression [tex]\rm x^2+6x+c[/tex]
It is required to find the value of c to make the above expression a perfect square.
A quadratic equation is a second-degree algebraic equation represented by the:
[tex]\rm Ax^2+Bx+C=0[/tex] ........(1)
Where A, B, and C are the constants and [tex]\rm A\neq 0[/tex]
We have a quadratic expression:
[tex]\rm x^2+6x+c[/tex]
To make the above expression a perfect square the value of c will be:
[tex]\rm c = (\frac{B}{2A} )^2[/tex] where B = 6, and A = 1
[tex]\rm c = (\frac{6}{2\times1} )^2 \Rightarrow 9[/tex]
If [tex]\rm\rm x^2+6x+c= (x+d)^2[/tex]
[tex]\rm\rm x^2+6x+c= x^2+2dx+d^2[/tex] put the value of 'c', we get:
[tex]\rm\rm x^2+6x+9= x^2+2dx+d^2[/tex]
By comparing both sides, we get:
2d = 6 (Coefficient of the x)
d = 3
Thus, the value of 'c' and 'd' are 9 and 3 respectively in the given equation [tex]\rm\rm x^2+6x+c= (x+d)^2[/tex]
Learn more about quadratic equations here:
brainly.com/question/2263981
What value of c makes x2 + 6x + c a perfect square trinomial?
-------------------
c =
✔ 9
-------------------
If x2 + 6x + c = (x + d)2, then
-------------------
d =
✔ 3
-------------------
