Question

find the quadratic polynomial whose zeroes are 1/4 and -1/5​

Answer 1

Answer:

sum of zeroes = 1/4 - 1/5 = 5-4/20 = 1/20. (bcoz LCM of 5 and 4 is 20)

product of zeroes = 1/4 * (-1/5) = -1/20

so polynomial formed:

x² - (1/20)x -1/20

Hope this helps ☺️

Answer 2

Step-by-step explanation:

Given:-

zeroes are 1/4 and -1/5

To find:-

find the quadratic polynomial whose zeroes are 1/4 and -1/5

Solution:-

Given zeroes are 1/4 and -1/5

Let the zeores be α and β

α = 1/4

β = -1/5

Sum of the zeores = α + β

=(1/4)+(-1/5)

LCM of 4 and 5 = 20

=> (5-4)/20

=> 1/20

Product of the zeroes =αβ

=> (1/4)(-1/5)

=>-1/20

we know that

α and β are the zeores then the quadratic polynomial is

K[x^2-(α + β)x +αβ]

=> K[x^2-(1/20)x+(-1/20)]

=>K[(20x^2-x-1)/20]

If K = 20 then

The required Polynomial = 20x^2-x-1

Answer:-

The quadratic polynomial for the given zeroes is

20x^2-x-1

Used formula:-

α and β are the zeores then the quadratic polynomial is

K[x^2-(α + β)x +αβ]