Question

find a quadratic polynomial,the sum and product of whose zeroes are 3 and 0

Answer 1

Let the Quadratic polynomial be ax^2 + bx + c.

Given sum of zeroes = 3

-b/a = 3

-b/1 = 3

b = -3.

Given product of zeroes = 0

c/a = 0

c/1 = 0

c = 0.

Therefore, the required polynomial = ax^2 + bx + c

= > x^2 + (-3)x + 0

= > x^2 - 3x

Hope this helps!

Answer 2

Hey !!

Let alpha and beta are the two zeroes of polynomial P ( x ).

Given :-

Sum of zeroes = 3

Alpha + Beta = 3 ---------(1)

And,

Product of zeroes = 0

Alpha × Beta = 0 ----------(2)

Therefore,

Required quadratic polynomial = X² - ( Sum of zeroes ) × X + Product of zeroes.

=> X² - ( 3 ) × X + 0

=> X² - 3X.

Hence,



Required Polynomial = X² - 3X.