Zeroes of a Polynomial

Q. t2-15 find the zeroes of quadratic polynomial and verify the relationship between the zeroes and its coefficient

Q. Find the zeroes of the quadratic polynomial 3x2 – 75 and verify the relationship between the zeroes and the coefficients.

Q.

The zeroes of the polynomial $x^2-2x-3$ are ____

1. -3, 1
2. -3, -1
3. 3, -1
4. 3, 1

Q. Find the zeroes of the following quadratic polynomial.
$x^2-2x-8$

1. -4 and 2
2. -4 and -2
3. 4 and -2
4. 4 and 2

Q.

If 1 is a zero of the polynomial $a{x}^2-3(a-1)x-1$ then find the value of a.

Q.

Find the zeroes of polynomial $2x^2-25.$

Q. Identify the number of zeroes of the polynomial represented by the graph shown below.

1. 0
2. 3
3. 2
4. 1

Q. if the product of zeroes of the polynomial (ax^2-6x-6) is 4 then the value of a is

Q.

Determine which of the following polynomials has (x+1) as a factor:
(i) $x^3$+$x^2$+x+1 (ii) $x^4$+$x^3$+$x^2$+x+1

Q. Find the value of a and b, if they are the zeroes of polynomial x^2 + ax + b.

Q. If the polynomial $6x^4+8x^3+17x^2+21x+7$ is divided by another polynomial $3x^2+4x+1$, the remainder comes out to be $ax+b$, find a and b.
[4 MARKS]

Q. Question 6
For which values of a and b, the zeroes of $q\left(x\right)=x^3+2x^2+a$ are also the zeroes of the polynomial $p\left(x\right)=x^5–x^4–4x^3+3x^2+3x+b?$ which zeroes of p (x) are not the zeroes of q(x)?

Q.

In the figure, the graph of a polynomial p(x) is shown. The number of zeroes of p(x) is:

1. 2

2. 4

3. 3

4. 1

Q. How to find zeros of polynomial 2x³-9x²+x+12

Q.

A polynomial of degree of n can have at most ______ number of zeroes.

1. n+1

2. n-1

3. n

4. can't say

Q. find the zeroes of the quadratic polynomial whose product and sum of the zeroes are 23 and 10 respectively. And also find the polynomial.

Q. 23.Find non zero values for p and q for which p and q are zeroes of x2+px+q

Q. If x/y+y/x=-1 (where, x, y is not equal to zero), then find the value of x^3-y^3.

Q.

Find two solutions for each of the following equations: $2x-5y=0$

Q.

If $\alpha ,\beta$ and $\gamma$ are the zeroes of the polynomial $f\left(x\right)=a{x}^3+b{x}^2+cx+d$, then $\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }$ is _____.

1. $\frac{c}{d}$

2. $\frac{a}{d}$

3. $-\frac{c}{d}$

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

Q.

Divide the polynomial $3x^4-4x^3-3x-1$ by x-1 and then find the remainder.

1. -4

2. -5

3. -6

4. -7

Q.

If $f:(–1,1)\to R$ be a differentiable function with $f\left(0\right)=–1andf\left(0\right)=1.$ Let $g\left(x\right)={\left[f\right\{2f\left(x\right)+2\}]}^2$. Then, $g\left(0\right)$is equal to

Q.

Find zeros of f(x)= x³ - 5x² - 16x + 80 , if it’s two zeros are equal in magnitude but opposite in sign

Q.

Number of polynomials having 3 and 7 as zeroes are?

1. 1

2. 2

3. 3

4. more than 3

Q. 25. If one zero of the polynomial (a2+9)x2 + 13x + 6a is reciprocal of the other, find the value of a

Q. Question 1
Determine which of the following polynomials has (x+1) a factor:
(i) $x^3+x^2+x+1$
(ii) $x^4+x^3+x^2+x+1$
(iii) $x^4+3x^3+3x^2+x+1$
(iv) $x^3-x^2-(2+\sqrt{2})x+\sqrt{2}$

Q. The polynomial x3-x2-x+1 has ____ distinct zeroes

Q.

Which one of the following statements is correct?

If $x^6+1$ is divided by $x-1$ reminder is $-1$.

1. True
2. False

Q. If 25 = ( 8 $\times$ Q ) + R
Find the value of Q and R.

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

Q. Find the zeros of the polynomial 2s2-(1+2√2)s+√2 and verify the relationship between the zeros and coefficient of the polynomial.