Zeroes of a Polynomial

Q.

Find the quadratic polynomial whose zeroes are $3$ and $-5$.

Q.

Find the zeroes of the polynomial $x^2+x-p\left(p+1\right)$.

Q.

Find the zeroes of the following polynomial by factorisation method: $t^3-2t^2-15t$.

Q. Find all the zeroes of the polynomial 2x4-9x3+5x2+3x-1 if two of its zeroes are (2+\sqrt3) and (2-\sqrt3)

Q.

Write the polynomial of whose zeroes are $-2\text{and}\frac{1}{3}$.

Q.

Verify whether the following are zeroes of the polynomial, indicated against them: $\mathrm{p}\left(\mathrm{x}\right)={\mathrm{x}}^2-1,\mathrm{x}=1,-1$

Q. What is the zero of the polynomial $p\left(x\right)=2x+5?$

1. $\frac{-5}{2}$
2. 2
3. 5
4. $\frac{2}{5}$

Q.

How many zeroes can a polynomial of degree $n$have?

Q.

Find the zero of the polynomial p(x)=ax, a≠0.

Q.

Find the zeroes of the quadratic polynomial $\sqrt{3x^2}-8x-4\sqrt{3}$.

Q.

Find a quadratic polynomial whose zeroes exceed the zeroes of x^2+5x+6 by 2 .

Q.

Find zero of the polynomial 2x-3

Q.

The zeros of the polynomial $p\left(x\right)=x^2-3x$ are
(a) 0, 0
(b) 0, 3
(c) 0, -4
(d) 3, -3

Q.

If a polynomial cuts the x-axis at 3 points and y-axis at 2 points, then the number of zeroes of the polynomial would be ___ .

Q. Find the zero of the polynomial $3x+2$.

1. $\frac{2}{3}$
2. $\frac{-2}{3}$
3. $\frac{3}{2}$
4. $\frac{-3}{2}$

Q.

For what value of k is the polynomial $p\left(x\right)=2x^3-k{x}^2+3x+10$ exactly divisible by (x+2)?
(a) $-\frac{1}{3}$
(b) $\frac{1}{3}$
(c) $3$
(d) $-3$

Q.

Find the zeros of the polynomial $4x^2-9.$

Q.

Verify whether the following are zeroes of the polynomial, indicated against them: $\mathrm{p}\left(\mathrm{x}\right)=5\mathrm{x}–\mathrm{\pi },\mathrm{x}=\frac{4}{5}$

Q. If -2 and -4 are the zeroes of a quadratic polynomial whose leading coefficient is 2, then find the value of (product of zeroes $\times$ coefficient of x).

[Note: In a polynomial, the term containing the highest power of x (i.e. a_nxⁿ) is the leading term, and we call a_n the leading coefficient.]

1. -16
2. 96
3. -96
4. 16

Q. Find the remainder when the polynomial $f\left(x\right)=2x^4-6x^3+2x^2-x+2$ is divided by x + 2

Q. How many zeroes does a constant polynomial has?

Q.

A quadratic polynomial, whose zeroes are $-3$ and $4$ is

1. $x^2-x+12$

2. $x^2+x+12$

3. $\frac{x^2}{2}-\frac{x}{2}-6$

4. $2x^2+2x-24$

Q. $\text{If twice the zero of the polynomial}\text{p(x) = 2x - 4 is equal to zero of the}\text{polynomial q(x) = 5x + a, then what}\text{is the value of a ?}$

1. 20
2. 10
3. -10
4. -20

Q.

The zero of the polynomial p(x) = ax+b is ______.

1. $\frac{a}{b}$

2. $-\frac{a}{b}$

3. $\frac{b}{a}$

4. $-\frac{b}{a}$

Q. Find the 0 of the polynomial r(x) = x2 + 3x

Q.

Verify that
(i) 4 is a zero of the polynomial, p(x) = x - 4.
(ii) -3 is a zero of the polynomial, q (x) = x + 3.
(iii) $\frac{2}{5}$ is a zero of the polynomial, $f\left(x\right)=2-5x$
(iv) $\frac{-1}{2}$ is a zero of the polynomial, g(y) = 2y + 1.

Q. if alpha&beta ate zeroes of the polynomial p(x)=x2-mx+n, thenfind the value of alpha/beta+beta/alpha

Q.

If 1 and -3 are the zeroes of a polynomial p(x) = x^3 - ax^2 - 13x + b ,

find the values of a and b.

Q.

If $2x^2-3xy+y^2+x+2y-8=0$, then $\frac{dy}{dx}$ is equal to

1. $\frac{\left(3y-4x-1\right)}{\left(2y-3x+2\right)}$

2. $\frac{\left(3y+4x+1\right)}{\left(2y+3x+2\right)}$

3. $\frac{\left(3y-4x+1\right)}{\left(2y-3x-2\right)}$

4. $\frac{\left(3y-4x+1\right)}{\left(2y+3x+2\right)}$

Q. $\text{What is the zero that is common to the}\text{polynomials}p\left(x\right)=x^2-2x+1\text{and}q\left(x\right)=x^2-3x+2?$

1. 2
2. 1
3. 3
4. 4