Which of the following is a cubic polynomial whose zeros are (−1), (−2) and(−3)?
x³−6
x³−6x²+6
x³−6x²+11x+6
x³−6x²-11x-6
2 and (−2) are two zeros of the polynomial (x²)²−5x²+4. What are the other two zeros of the polynomial?
1 , -1
1 , -2
-1 , 2
1 , 0
Find the zeroes of the polynomials f(y)=y³+y²−9y−9, if two zeroes are equal in magnitude but opposite in sign. α,−α,β
(1,−1,−3)
(+3,−3,−1)
(−2+√3,2−√3,−1)
None
If a and b are the roots of the equation3m²+6m−11, find a polynomial whose roots are 2a+1 and2b+1.
k(m²+3m−53/3)
k(m²+9m−41)
k(m²+9m+41)
k(m²--9m-41)
Which of the following is the division algorithm of polynomials, if dividend = f(x), divisor = p(x), quotient = q(x) and remainder = r(x)?
f(x)=r(x)p(x)+q(x)
f(x)=p(x)q(x)+r(x)
f(x)=p(x)q(x)-r(x)
None
Find the values of C for which the zeroes of the polynomial f(x)=x³+3x²+6x+C are in A.P.
-36
22
−√35
√21
α,βandγare the zeros of a cubic polynomial. Ifα+β+γ=3,αβ+βγ+γα=(−5)andαβγ=(−24), find the polynomial.
x³-3x²-5x+24
m³-3m²-5m-24
n³-2n²+7n+12
y³+6y²-10y-48
Which of the following is the graph of a linear polynomial?
None
α and βare the zeros of a polynomial, such that α+β=6and αβ=4. Identify the polynomial.
x²-6x+4
x²+8x+6
x²+16
x²-4
Identify the zeros of the cubic polynomial p(m)= m²− 8m²+19m−12 .
−1,−3,−4
0,−3,4
1,3,4
−1,1,12
The zeros of a cubic polynomial y³−6y²+11y+8 are m,m−a, m+a. What is the value of m?
3
2
1
0
Identify the quadratic polynomial with no zeros.
All
If a polynomial p(x) is divided by another polynomial g(x), with a quotient q(x) and remainder r(x), then p(x) = q(x) g(x) + r(x). What is the condition that r(x) must satisfy?
r(x)=0
r(x)=0or deg of r(x)>deg g(x)
Either r(x)=0or deg r(x)<deg (g(x))
r(x)=g(x)
Find the sum of zeros of the polynomial 7x²−17.
0
1
-1
2
If α and βare the zeros of ax²−a²x+a³ where a < 1, and a > 0 then, which of the following is correct?
α+β<αβ
α+β>αβ
β−α>αβ
α+β=αβ
What is the nature of the zeros of the quadratic polynomial 2x²+63x+ 63.
Both positive
Both negative
One positive, one negative
None
When is a real number 'a' called the zero of the polynomial f(x)?
f (0) = a
f = a
f = 0
f (0) = f
If α,β and γ are the zeros of p(x), which of the following is true?
p(x) = ( x−α )(x − β) (x − γ)
p(x) = ( x+α )(x − β) (x − γ)
p(x) = ( x−α )(x + β) (x − γ)
p(x) = ( x+α )(x + β) (x + γ)
Which of the following is not correct?
The degree of a zero polynomial is zero.
The degree of a cubic polynomial is 3.
A quadratic polynomial has a maximum of two zeros.
