Question

find a quadratic polynomial whose zeroes are 2 and _6​

Answer 1

$\huge{\boxed{\mathtt{\purple{Answer}}}}$

Given:
the quadratic polynomial whose zeroes are 2 and _6
To find :
The polynomial and verify the relationship.
Solving Question:
we are given the zeros of the polynomial, hence we can find the polynomial through these equations.
If α and β are the zeros
α + β = -b/a
α * β = c/a
Solution:
α + β = 2 + (-6)
= 2-6
= -4 = -b/a
⇒ a = 1 ; b = 4
α * β = 2 *(-6)
= -12 = c/a
⇒ c = -12
Standard form : ax² + (α + β )x + α*β
the equation becomes k(x² + 4x -12 ) , where 'k' is a constant.
Relationship ;
α + β = -4 = -b/a
α * β = -12 = c/a