Value of a polynomial

Q.

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorization

$\left(\frac{-8}{3}\right),\left(\frac{4}{3}\right)$

Q.

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

Q. One of the zeroes of the polynomial is $2x^2+7x–4$ is

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

Q.

Find the zeroes of the polynomial

$x^2-5x$

Q. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) $\frac{1}{4}$, $-1$ (ii) $\sqrt{2},\frac{1}{3}$ (iii) $0,\sqrt{5}$
(iv) $1,1$ (v) $\frac{-1}{4},\frac{1}{4}$ (vi) $4,1$

Q.

Find the zero of the polynomial in each of the following cases:
(i) $p\left(x\right)=x+5$
(ii) $p\left(x\right)=x-5$
(iii) $p\left(x\right)=2x+5$
(iv) $p\left(x\right)=3x-2$
(v) $p\left(x\right)=3x$
(vi) $p\left(x\right)=ax,a\ne 0$
(vii) $p\left(x\right)=cx+d,c\ne 0$ and $c,d$ are real numbers.

Q. How do you factor $x^2+5x-6$?

Q.

If $1$ and $-3$ are zeroes of the polynomial $p\left(x\right)=x^3-a{x}^2-13x+b$, find the values of $a$ and $b$.

Q. One of the zeroes of the polynomial is $2x^2+7x–4$ is

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

Q.

If $(x-1)$ is a factor of $a{x}^3-b{x}^2+cx$, what is the value of $a^3-b^3+c^3$?

1. 2abc

2. -2abc

3. 3abc

4. -3abc

Q. The zeroes of a polynomial $p\left(x\right)=a{x}^2+bx+2$ are 1 and 2
Which of the following are statements is/are true?

1. $a+b+2=0$
2. $a+2b+2=0$
3. $a+b+1=0$
4. $5a+3b+4=0$

Q. One of the zeroes of the polynomial is $2x^2+7x–4$ is

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

Q. If $x-2$ is a factor of $p\left(x\right)=a{x}^2+bx+3$, which of the following statements is true?

1. a + b = -3
2. 2a + 4b = 3
3. 4a + 2b = -3
4. 2a + 4b = -3

Q. If a polynomial $p\left(x\right)=x^2-ax+b$ has two zeroes 1 and 7, what is the value of $ab$?

1. 7
2. 42
3. 56
4. 8

Q. If a polynomial $p\left(x\right)=x^2-ax+b$ has two zeroes 1 and 7, what is the value of $ab$?

1. 8
2. 56
3. 42
4. 7

Q.

Show that $\mathrm{p}-1$is a factor of${\mathrm{p}}^{10}-1$and also of${\mathrm{p}}^{11}-1.$

Q.

If f(x) = 2x + 1, what is f(-3)?

1. 5

2. 7

3. -5

4. -7

Q.

If f(x) = 2x + 1, what is f(-5)?

1. -11

2. 9

3. -9

4. 11

Q. If f(x) = 3x - 5, what is the value of f(-2)?

1. 11
2. -11
3. -1
4. 1

Q. The value of the polynomial ‘3x’
at x = 1 is 1.

1. True
2. False

Q. The zero of the polynomial $p\left(x\right)=4x+3$ lies at $x$ = .

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

Q.

What is (5x-7) when x = -1?

1. -2

2. 12

3. -12

4. 2

Q. ‘$x^{-2}+3$’ is a polynomial.

1. True
2. False

Q. If a polynomial $p\left(x\right)=x^2-ax+b$ has two zeroes 1 and 7, then the value of $ab$ is .

1. 8
2. 42
3. 56

Q. If a polynomial $p\left(x\right)=x^2-ax+b$ has two zeroes 1 and 7, then the value of $ab$ is .

1. 8
2. 42
3. 56

Q.

How do you factor $x^4-y^4$ ?

Q. Verify that $3,-2,1$ are the zeroes of the cubic polynomial $p\left(x\right)=(x^3-2x^2-5x+6)$ and verify the relationship between its zeroes and coefficients.

Q. If a polynomial $p\left(x\right)=x^2-ax+b$ has two zeroes 1 and 7, what is the value of $ab$?

1. 8
2. 56
3. 42
4. 7

Q. Maximum number of zeroes that a polynomial can have is equal to the degree of that polynomial.

1. True
2. False