Cubic Polynomial
Trending Questions
Q.
If , then the possible value of is
Q. If α, β, γ are the roots of x3+3x2+2=0 then find the equation whose roots are αβ+γ, βγ+α, γα+β
- 2x3+33x2−6x+2=0
- 2x3+33x2+6x+2=0
- 2x3+33x2+6x−2=0
- 2x3+33x2−6x−2=0
Q.
If two roots of the equation x3−3x+2=0 are same, then the roots will be
- 2, 3, 3
-2, -2, 1
2, 2, 3
1, 1, -2
Q. Let p, q, r be the roots of x3+2x2+3x+3=0, then which of following is/are correct?
- (pp+1)3+(qq+1)3+(rr+1)3=38
- pp+1+qq+1+rr+1=5
- (pp+1)3+(qq+1)3+(rr+1)3=44
- pp+1+qq+1+rr+1=6
Q. If p ϵ [−1, 1], then the value of x for which 4x3−3x−p=0 has a root lies in
- [12, 1]
- [−1, 1]
- [0, 3]
- [0, 12]
Q.
If the sum of two of the roots of x3+px2+qx+r=0 is zero, then pq =
r
2 r
- r
- 2 r
Q.
If are in A.P., then …..
Q. From the graph of the cubic polynomial f(x)=x3−5x2+8x−4, the number of distincts zeroes are
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1462903/original_cube2.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1462903/original_cube2.png)
Q. If one of the roots of the quadratic equation x2−x−1=0 is α, then its other root is
- α3−3α
- α3−2α
- α2−2α
- α2−3α
Q. Find the equation whose roots are the cubes of the roots of \(x^3 + 3x^2 + 2 =0\)
Q. If x3+5x2+px+q=0 and x3+7x2+px+r=0 have two roots in common and their third roots are γ1 and γ2 respectively, then the value of |γ1+γ2| is
Q. If x3+5x2+px+q=0 and x3+7x2+px+r=0 have two roots in common and their third roots are γ1 and γ2 respectively, then the value of |γ1+γ2| is
- 5
- 13
- 17
- 12
Q. Which among the following is a cubic polynomial?
- 2x3+5x2+6x+1
- x4+3x3+4x2−5x+4
- x2+x+1
- x3−3x−1+5
Q. The number of distinct real roots of the cubic polynomial equation x3−3x2+3x−1=0 is
- 1
- 2
- 0
- 3
Q. The cubic polynomial p(x) satisfies p(0)=1, p(1)=20, p(2)=40, p(3)=60. Then the value of p(4) is
- 78
- 81
- 79
- 80
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 an into function
- f(x)=4 has only one solution
- f(x) is a one-one function
- f(x) is an onto function
Q.
If α, β, γ are the roots of x3+px2+qx+r=0, then find the value of
(α−1βγ)(β –1γα)(γ –1αβ)
(r3−1)r2
(r3+1)r2
−(r+1)3r2
None of these
Q.
__
If α, β and γ are the roots of the equation x3−3x2+5x−9=0 then the value of the expression
(α+β−γ)(β+γ−α)(γ+α−β).
Q. Which of the following are the common zeros of the polynomials (x2−16)(x+9) and (x2−81)(x+4) ?
- −4
- 4
- −9
- 9
Q.
Sum of the real roots in the equation x2|x|−17x2+95|x|−175=0 is:
34
0
None
17
Q. Which among the following is a cubic polynomial?
- 2x3+5x2+6x+1
- x2+x+1
- x4+3x3+4x2−5x+4
- x3−3x−1+5
Q. If x3−x2+5x−1=0 has roots α, β, γ and x3+ax2+bx+c=0 has roots αβ, βγ, γα, then the value of (a+b+c) is
- 3
- 7
- −5
- −1
Q. Let p, q, r be roots of cubic equation x3+2x2+3x+3=0, then
- (pp+1)3+(qq+1)3+(rr+1)3=44
- (pp+1)3+(qq+1)3+(rr+1)3=38
- pp+1+qq+1+rr+1=5
- pp+1+qq+1+rr+1=6
Q. If x3−2x2−5x+6=0 and a, b, c are its roots, then match the following with their respective answers.
- 20
- 8
- 14
Q. The equation x34(log2x)2+log2x−54=√2 has
- complex roots
- exactly three real solutions
- exactly one irrational solution
- atleast one real solution
Q. Let x3+ax2+bx+c=0 has roots α, β, γ. If α+2=1α2, β+2=1β2 and γ+2=1γ2, then the value of 3a+2b+c is
Q. If the zeroes of monic cubic polynomial are 3, 5 and 6, then the cubic polynomial is
- 2x3−28x2+126x−180
- x3−14x2+63x−90
- 3x3−42x2+189x−270
- 2x3−14x2+60x−78
Q.
Divide 4x3+12x2+11x+3 by x+1 and then find the quotient.
2x2+3x+3
4x2+6x+1
8x2+11x+3
4x2+8x+3
Q. If the zeroes of monic cubic polynomial are 3, 5 and 6, then the cubic polynomial is
- x3−14x2+63x−90
- 2x3−14x2+60x−78
- 2x3−28x2+126x−180
- 3x3−42x2+189x−270
Q. If x1, x2, x3 be the roots of the equation x3−x+1=0, then the value of (1+x11−x1)(1+x21−x2)+(1+x11−x1)(1+x31−x3)+(1+x21−x2)(1+x31−x3) is