Quadratic equation is the polynomial equation in which the highest degree of its variable is two.The highest degree of the equation given in option 1 is four and thus it is a quadratic equation. Hence, option 1 is the correct option.
Quadratic equation is the polynomial equation in which the highest degree of its variable is two.
Let's check all the given options one by one whether it is a quadratic equation or not.
Option 1-
[tex]6(x + 2)^2 + 8x + 2 + 1 = 0[/tex]
simplify the above equation using the algebraic formula of the whole square, we get,
[tex]6(x^2 + 4x+4) + 8(x + 2) + 1 = 0[/tex]
[tex]6x^2 + 24x+24 + 8x + 16 + 1 = 0[/tex]
[tex]6x^2 + 32x+41 = 0[/tex]
The highest degree of the equation given in option 1 is four and thus it is a quadratic equation.
Option 2-
[tex]6x^4+7x^2-3=0[/tex]
The highest degree of the equation given in option 2 is four and thus it is not a quadratic equation. hence option 2 is incorrect.
Option 3-
[tex]5x^6+x^4+12=0[/tex]
The highest degree of the equation given in option 3 is six and thus it is not a quadratic equation. hence option 3 is incorrect.
option 4-
[tex]x^9+x^3-10=0[/tex]
The highest degree of the equation given in option 4 is nine and thus it is not a quadratic equation. hence option 4 is incorrect
Hence, the highest degree of the equation given in option 1 is four and thus it is a quadratic equation. Hence, option 1 is the correct option.
For more about the quadratic equation follow the link given-https://brainly.com/question/17177510
