1
1

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 
  •  $\frac{1}{4}, -1$ 
  •  $\sqrt{2}, \frac{1}{3}$ 
  •  $0, \sqrt{5}$ 
  •  $1, 1$
  • $ - \frac{1}{4}, \frac{1}{4}$ 
  •  $4, 1$
Posted by: | Created at: Last updated: |
Tags: Class X Maths Class X

This Question has 3 answers.

1
The general form of a quadratic polynomial when the sum and product of its zeroes are given is:

$x^2 - (\text{sum of zeroes})x + (\text{product of zeroes})$

Now, applying this formula for each given pair:

1) Sum = $\frac{1}{4}$, Product = $-1$
$x^2 - \frac{1}{4}x - 1$

2) Sum = $\sqrt{2}$, Product = $\frac{1}{3}$
$x^2 - \sqrt{2}x + \frac{1}{3}$

3) Sum = $0$, Product = $\sqrt{5}$
$x^2 + \sqrt{5}$

4) Sum = $1$, Product = $1$
$x^2 - x + 1$

5) Sum = $- \frac{1}{4}$, Product = $\frac{1}{4}$
$x^2 + \frac{1}{4}x + \frac{1}{4}$

6) Sum = $4$, Product = $1$
$x^2 - 4x + 1$

Thus, these are the required quadratic polynomials. 
Posted by: | Created at: Last updated: |
1
use the formula x2−(sum of zeroes)x+(product of zeroes)=0. Here, 

the sum of zeroes is 14, and the product of zeroes is −1. 

Substituting these values, the polynomial is: x2−14x−1=0.
Posted by: | Created at: Last updated: |
1
A quadratic polynomial with sum S and product P of its zeroes is given by:

x2−Sx+P For each given sum and product:

3. Given S=0,P=5 x2−(0)x+5=x2+5

4. Given S=1,P=1 x2−(1)x+1=x2−x+1

5. Given S=−14,P=14 x2−(−14)x+14=x2+14x+14

6. Given S=4,P=1 x2−(4)x+1=x2−4x+1
Posted by: | Created at: Last updated: |

Similar Questions

Add Answer / Comment

Captcha Image
Use of Basic Formatting such as Bold / Italic / Underline / Ordered or Unordered List is allowed.