# Zeroes of a Quadratic Polynomial

## Trending Questions

**Q.**The quadratic polynomial whose sum and product of the zeroes is 9 and 19 respectively is

- x2-9x+19
- x2+9x-19
- -x2-9x+19
- 9x2-9x+19

**Q.**If 1 and -2 are two zeroes of the polynomial x3−4x2−7x+10, then the third zero is

- 1
- 5
- -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 ?

$0$

$1$

Any real number

Not defined

**Q.**

If \times p(x)=x3−3x2+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 x4−x3−3x2+3x are 0, √3 and −√3 then find the fourth zero.

**Q.**

What is integral value?

**Q.**Find the zeroes of the following quadratic polynomial: 6x2+x−5

- 56, −1
- 12, 1
- 6, 5
- 2, 1

**Q.**Obtain all other zeroes or the polynomial x4+6x3+x2−24x−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 ax2−3x+b, then find the value of a - b.

- 0
- 1
- - 1
- 2

**Q.**

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

Only one solution

One two solutions

Infinite number of solutions

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)(x2−x−x4+1) is

- 2
- 3
- 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.

- 300kmhr
- 400kmhr
- 420kmhr
- 320kmhr

**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 3x4+6x3−2x2−10x−5, if two of its zeroes are √53 and −√53.

**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 :

(i)2x3+x2−5x+2;12.1, −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 :

(ii)x3−4x2+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.

−14, 14

**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 (2x4−9x3+5x2+3x+1) if two of its zeroes are (2+√3) and (2−√3).

**Q.**If 1 and -2 are two zeroes of the polynomial x3−4x2−7x+10, find its third zero.

- - 1
- 5
- 1
- - 5

**Q.**The degree of the polynomial 4x4−3x2+x+6 is

- 7
- 1
- 4
- 2

**Q.**

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

Only one solution

No solution

None of these

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

- 0
- 1
- 4
- 2