Zeroes of a Quadratic Polynomial

Q. The quadratic polynomial whose sum and product of the zeroes is 9 and $\frac{1}{9}$ respectively is .

1. x2-9x+19
2. x2+9x-19
3. -x2-9x+19
4. 9x2-9x+19

Q. If 1 and -2 are two zeroes of the polynomial $x^3-4x^2-7x+10$, then the third zero is.

1. 1
2. 5
3. -5

Q.

Use the factor theorem to factorize the polynomial $x^3-13x-12$ completely. Hence solve the corresponding polynomial equation.

Q.

Zero of the zero polynomial is ?

1. $0$

2. $1$

3. Any real number

4. Not defined

Q.

If \times $p\left(x\right)=x^3-3x^2+2x$, find p(0), p(1), p(2). What do you conclude?

Q.

Write four solutions for the following equations: $x=4y$

Q. If three zeroes of a polynomial $x^4-x^3-3x^2+3x$ are 0, $\sqrt{3}$ and $-\sqrt{3}$ then find the fourth zero.

Q.

What is integral value?

Q. Find the zeroes of the following quadratic polynomial: $6x^2+x-5$

1. $\frac{5}{6},-1$
2. $\frac{1}{2},1$
3. 6, 5
4. 2, 1

Q. Obtain all other zeroes or the polynomial $x^4+6x^3+x^2-24x-20,$ if two of its zeroes are + 2 and -5.

Q.

Find a quadratic polynomial whose sum and product of zeroes are -4 & 3 respectively. [1 MARK]

Q.

Question 2 (vi)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

4, 1

Q. If x = 2 and x = 1 are the zeroes of the quadratic polynomial $a{x}^2-3x+b,\text{then find the value of a - b}$.

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

Q.

The equation $x+2y+2z=1$ and $2x+4y+4z=9$ have

1. Only one solution

2. One two solutions

3. Infinite number of solutions

4. None of these

Q.

For what value of $a,$the system of linear equations; $ax+3y=a-3;12x+ay=a$ has no solution?

Q.

Question 2 (vi)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

4, 1

Q. The degree of the polynomial $(x+1)(x^2-x-x^4+1)$ is

1. 2
2. 3
3. 4
4. 5

Q. An aeroplane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr than its usual speed. Find its usual speed.

1. $300\frac{km}{hr}$
2. $400\frac{km}{hr}$
3. $420\frac{km}{hr}$
4. $320\frac{km}{hr}$

Q. Question 4 (iv)
Find the values of p for the following pair of equations 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.

Q.

Question 3
Obtain all other zeroes of $3x^4+6x^3-2x^2-10x-5$, if two of its zeroes are $\sqrt{\frac{5}{3}}and-\sqrt{\frac{5}{3}}$.

Q. (1)
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case :
$\left(i\right)2x^3+x^2-5x+2;\frac{1}{2}.1,-2$

(2)
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case :
$\left(ii\right)x^3-4x^2+5x-2;2,1,1$

Q.

Question 2 (iv)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

1, 1

Q. Question 4 (iii)
Find the value(s) of p for the following pair of equations – 3x + 5y = 7 and 2px – 3y = 1,
If the lines represented by these equations are intersecting at a unique point.

Q.

Question 2 (v)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

$\frac{-1}{4},\frac{1}{4}$

Q.

Find the value of $k$ for which the following system of equations has infinitely many solutions

$(k-1)x+3y=7;(k+1)x+6y=(5k-1)$$=3$

Q. Find all zeroes of the polynomial $(2x^4-9x^3+5x^2+3x+1)$ if two of its zeroes are $(2+\sqrt{3})$ and $(2-\sqrt{3})$.

Q. If 1 and -2 are two zeroes of the polynomial $x^3-4x^2-7x+10$, find its third zero.

1. - 1
2. 5
3. 1
4. - 5

Q. The degree of the polynomial $4x^4-3x^2+x+6$ is

1. 7
2. 1
3. 4
4. 2

Q.

Equations x+y=2, 2x+2y=3 will have

1. Only one solution

2. No solution

3. None of these

4. Many finite solutions

Q. Find the valueof k for which the following system of equations has no solution:
2x + 3y - 5 = 0 and kx + 6y - 8 = 0

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