Question

The equation $2x^3-3x^2-12x+1=0$ has in the interval $(-2,1)$

• A. no real root
• B. exactly one real root
• C. exactly two real roots
• D. all three real roots

Answer 1

The correct option is A no real root

$f\left(x\right)=2x^3-3x^2-12x+1$

in the interval $(-2,1)$

$f(-2)=2\times {(-2)}^3-3\times \left({-2}^2\right)-12\times (-2)+1$

$=-16-12+24+1$

$=-28+25=-3$

$f\left(1\right)=2\times 1-3\times 1-12\times 1+1$

$=2-3-12+1$

$=3-3-12=-12$

Both $f(-2)$ and $f\left(1\right)$ are less than zero

$\therefore$ fn has no real roots in this region.