Question

Q.102 The smallest +ve root of x3 - 5x + 3 = 0 lies between
A. 2 and 3
C. 1 and 2
B. 0 and 1

D. None of these​

Answer 1

Answer:

D. None of these

Step-by-step explanation:

The equation is not factoriseable

Answer 2

Answer:

The smallest +ve root of $x^3 - 5x + 3 = 0$ lies between option B i.e 0 and 1

Step-by-step explanation:

• The method used for finding the root is the hit and trial method.
• Since the equation is cubic it should have 3 roots.

1. 1st Trial

• let x =0, the value of equation  $x^3 - 5x + 3$ is 3

• let x =1, the value of the equation    $x^3 - 5x + 3$ is -1

• Since the value of the equation changes the sign, thus one root lies between 0 and 1

    2. 2nd Trial

• let x =2, the value of the equation    $x^3 - 5x + 3$ is 1
• Since the sign of the values of the equation again changes between 2 and 3, another root lies between 2 and 3

   3. 3rd Trial

• let x =3, the value of the equation   $x^3 - 5x + 3$ is 15
• let x =4, the value of the equation    $x^3 - 5x + 3$ is 47
• Now since the sign of the value does not change. The third root cant is positive.

Conclusion

The smallest positive root lies between 0 and1