Nature of Roots of a Cubic Polynomial Using Derivatives
Trending Questions
Q.
Find the equation whose roots are equal in magnitude but opposite in sign to the roots of the equation x5- 3 x3 + 2 x2 + 4x + 1 = 0.
x5 - 3x3 - 2x2 + 4x - 1 = 0
x5 - 3x3 + 2x2 + 4x + 1 = 0
x5 + x3 + x2 + x + 1 = 0
x5 + 2x3 + 3x2 + 5x - 1 = 0
Q.
If ∝, β are the roots of the equation 2x2 - 3x - 5 = 0, then the equation whose roots are 5∝ , 5β is :
x2 - 3x - 10 = 0
x2 + 3x - 10 = 0
x2 + 3x + 10 = 0
x2 - 3x + 10 = 0
Q. Write the number of real roots of the equation .
Q.
Interval in which ‘a′ lies so that x3–3x+a=0 has three real and distinct roots.
(-1, 1)
(-2, 2)
(-1 , 2)
(-2, 1)
Q. A function f:R→R is defined as f(x)=−x3+3x2−2x+4. Which of the following is true about the function f(x)?
- f(x) is a one-one function
- f(x)=4 has only one solution
- f(x) is an into function
- f(x) is an onto function
Q.
If one root of the equation ax2 + bx + c = 0 be n times the other root, then
nb3 = ac(n+1)2