Question

If 3 and 4 are sum of the root and product of the root respectively then the required polynomial is

Answer 1

the required polynomial is

x^2- 3 x+4

Answer 2

Given :   3 and 4 are sum of the root and product of the root respectively

To find :  required polynomial

Solution:

sum of the root  = 3

Products of roots  = 4

Required polynomial is  x ² - (sum of roots)x  + (product of roots) = 0

=> x²  - 3x  + 4  = 0

another way

lets roots are  α  & β

then polynomial is

(x - α)(x - β)  

Sum of roots = 3

=> α + β = 3

Product of roots = 4

=> αβ = 4

polynomial is  (x - α)(x - β)  

= x² - x(α + β ) + αβ

= x² - 3x + 4

x² - 3x + 4   is required polynomial

Learn more:

If the sum of roots is equal to the squares of their reciprocals of a ...

https://brainly.in/question/14131391

the sum of a number and its positive square root is 6 / 25 find the ...

https://brainly.in/question/8283141

i) If the sum of the roots of the quadratic equationax² + bx + c = 0 is ...

https://brainly.in/question/15319973