How can I find the intervals $a
did I need to solve the given equation.then it would be a very lengthy process.is there any short process?can anyone help me?thanks.
How can I find the intervals $a
did I need to solve the given equation.then it would be a very lengthy process.is there any short process?can anyone help me?thanks.
Let $f(x) = x^4 -12x + 5$. $f(\text{negative number}) > 0$ $f(0) = 5$, $f(1) = -6$, $f(2) = -3$, $f(3) = 50$.
Hence, there are roots between $[0,1]$ and $[2,3]$.
Further $f'(x) = 4x^3 - 12$. Hence, the function is increasing for $x>\sqrt[3]{3}$ and decreasing for $x< \sqrt[3]{3}$.
Hence, there are only two real roots; one in the interval $[0,1]$ and the other in the interval $[2,3]$.