A zero of *x*^{3 }+ 64 is

**A. ** 0

**B. ** 4

**C. ** 4i

**D. ** -4

**Answer : ****Option D**

**Explaination / Solution: **

Workspace

Report

If *f *and *g *are
polynomials of degrees *m *and *n *respectively, and if *h*(*x*)
= ( *f *o *g *)(*x*) , then the degree of *h *is

**A. ** *mn*

**B. ** *m* + *n*

**C. ** *m*^{n}

**D. ** *n*^{m}

**Answer : ****Option A**

**Explaination / Solution: **

Workspace

Report

A polynomial equation in *x
*of degree *n *always has

**A. ** *n* distinct roots

**B. ** *n* real roots

**C. ** *n* imaginary roots

**D. ** at most one root.

**Answer : ****Option C**

**Explaination / Solution: **

A polynomial of degree n always has n roots

A polynomial of degree n always has n roots

Workspace

Report

If *α *, *β *, and *γ *are the zeros of *x*^{3
}+ *px*^{2 }+ *qx *+ *r *, then is

**A. ** -*q*/*r*

**B. ** -*p*/*r*

**C. ** *q*/*r*

**D. ** -*q*/*p*

**Answer : ****Option B**

**Explaination / Solution: **

Workspace

Report

According to the rational
root theorem, which number is not possible rational zero of 4*x*^{7 }+ 2*x*^{4 }−10*x*^{3 }− 5 ?

**A. ** −1

**B. ** 5/4

**C. ** 4/5

**D. ** 5

**Answer : ****Option B**

**Explaination / Solution: **

Workspace

Report

The polynomial *x*^{3
}− *kx*^{2 }+ 9*x* has three real zeros if and only if, *k *satisfies

**A. ** |*k|* ≤ 6

**B. ** *k* = 0

**C. ** |*k|* > 6

**D. ** |*k|*
≥ 6

**Answer : ****Option D**

**Explaination / Solution: **

Workspace

Report

The number of real numbers
in [0, 2*π*] satisfying sin^{4 }*x
*− 2 sin^{2 }*x *+1 is

**A. ** 2

**B. ** 4

**C. ** 1

**D. ** ∞

**Answer : ****Option A**

**Explaination / Solution: **

Workspace

Report

If *x*^{3 }+12*x*^{2 }+10*ax *+1999 definitely has a
positive zero, if and only if

**A. ** a ≥ 0

**B. ** a > 0

**C. ** a < 0

**D. ** a ≤ 0

**Answer : ****Option C**

**Explaination / Solution: **

Workspace

Report

The polynomial *x*^{3
}+ 2*x *+ 3 has

**A. ** one negative and two imaginary zeros

**B. ** one positive and two imaginary zeros

**C. ** three real zeros

**D. ** no zeros

**Answer : ****Option A**

**Explaination / Solution: **

Workspace

Report

The number of positive
zeros of the polynomial is

**A. ** 0

**B. ** *n*

**C. ** < *n*

**D. ** *r*

**Answer : ****Option B**

**Explaination / Solution: **

Workspace

Report