Answer:
<em>x ≈ - 0.7 ≈ 0.7; Option A </em>
Step-by-step explanation:
Let us substitute f ( x ) with 0, as to find the " real zero value( s ) " of the function;
0 = 3x^4 + x^2 - 1 ⇒ Swap sides, as such,
3x^4 + x^2 - 1 = 0 ⇒ Rewrite equation with u being = x^2, u^2 = x^2,
3u^2 + u - 1 = 0 ⇒ And solve for u by completing the square,
3u^2 + u = 1 ⇒ Divide either side by 3,
u^2 + u / 3 = 1 / 3 ⇒ Write equation in the form x^2 + 2ax + a^2 = ( x + a )^2, solving for a,
2au = 1 / 3u,
a = ( 1 / 3u ) / 2u,
a = 1 / 6 ⇒ Add value of a^2 to either side of equation,
u^2 + u / 3 + ( 1 / 6 )^2 = 13 / 36,
( u + 1/ 6 )^2 = 13 / 36 ⇒ Solve for u,
u = ( √13 - 1 ) / 6, and u = ( - √13 - 1 ) / 6 ⇒ Substitute value of u back into first equation to solve for x,
x = √( - 1 + √13 ) / 6 ), x = - √( - 1 + √13 ) / 6 ), x = √( - 1 - √13 ) / 6 ), x = - √( - 1 - √13 ) / 6 ) ⇒ Convert to approximate decimal form,
x = 0.6589.... = - 0.6589....
<em>Answer; x ≈ - 0.7 ≈ 0.7; Option A </em>
