Question

x^2+6x+9 find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their Coefficient​

Answer 1

${x}^{2} + 6x + 9 \\ = {x}^{2} + 3x + 3x + 9 \\ = x(x + 3) + 3(x + 3) \\ = (x + 3)(x + 3) \\ = (x + 3)^{2}$

Answer 2

Step-by-step explanation:

=  x² + 6x + 9

By splitting the middle term,

=  x² + 3x + 3x + 9

=  x( x + 3 ) + 3( x + 3 )

= ( x + 3 ) ( x + 3 )

Therefore,

zeros are, α = -3 ; β = -3

Co-efficients, a = 1; b = 6; c = 9;

Therefore,

Sum of zeros

= α + β = -b/a

= -3 - 3 = -6/1

= -6 = -6

Prodct of zeros

= αβ = c/a

= -3 × ( -3 ) = 9/1

= 9 = 9

Therefore, relationship between zeros and co-efficients verified.