which equation is quadratic in form?\n$3x^{5}+8x^{3}+6 = 0$\n$6x^{4}+7x^{2}-3 = 0$\n$5x^{6}+x^{4}+12 =…

which equation is quadratic in form?\n$3x^{5}+8x^{3}+6 = 0$\n$6x^{4}+7x^{2}-3 = 0$\n$5x^{6}+x^{4}+12 = 0$\n$x^{9}+x^{3}-10 = 0$

Answer

B. $6x^{4}+7x^{2}-3 = 0$

A quadratic - form equation is of the form $au^{2}+bu + c=0$, where $u$ is an algebraic expression.

For $3x^{5}+8x^{3}+6 = 0$, the highest - power relationship does not follow the quadratic - form pattern.

Let $u = x^{2}$, then $6x^{4}+7x^{2}-3=6u^{2}+7u - 3 = 0$, which is in quadratic form.

For $5x^{6}+x^{4}+12 = 0$, if we let $u=x^{2}$, we get $5u^{3}+u^{2}+12 = 0$, not quadratic.

For $x^{9}+x^{3}-10 = 0$, the power relationship is not quadratic - form.