Question

Find the quadratic polynomial whose zeroes are 2 and _6 respectively, verify the relation between the coefficient and zeroes of the polynomials

Answer 1

Heya see the pic below for solution. Hope it helps you. Kindly mark it brainliest.

The verification is indeed in the process.

Answer 2

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