Question

Which equation is quadratic in form?

Answer 1

we know that

A quadratic equation is a polynomial with an order of two. Its general form is

$ax^{2} + bx + c = 0$

case a) $6(x + 2)^{2} + 8x + 2 + 1 = 0$

$6(x + 2)^{2} + 8x + 2 + 1 = 0 \\ 6(x^{2} +4x+4)+8x+3=0\\ 6x^{2} +24x+24+8x+3=0\\ 6x^{2} +32x+27=0\\\\ a=6\\ b=32\\ c=27$

The case a) is a quadratic equation

case b) $6x^{4} + 7x^{2} - 3 = 0$

The case b) is a grade $4$ polynomial

case c) $5x^{6} + x^{4} + 12 = 0$

The case c) is a grade $6$ polynomial

case d) $x^{9} + x^{3} - 10 = 0$

The case d) is a grade $9$ polynomial

therefore

the answer is

$6(x + 2)^{2} + 8x + 2 + 1 = 0$

Answer 2

Answer:

$6(x+2)^2 + 8x +2+1= 0$

Step-by-step explanation:

If an equation is quadratic it means that the greatest exponent to which the variable is raised is 2

$6(x+2)^2 + 8x +2+1= 0\\6(x+2)^2 +8x+3=0$

we solve the power

$(a+b)^2= a^2 +2ab+b^2$

$6(x^2+4x+4)+8x+3 \\6x^+24x+24+8x+3$

In this case the greatest exponent to which the x is raised is 2

Therefore it is is a quadratic equation

$6x^4+7x^2-3=0$

$5x^6+x^4+12=0$

$x^9+x^3-10=0$

In these cases the greatest exponent to which the x is elevated is greater than two therefore it is not a square equation