Question

if alpha and beta are the zeroes of the polynomial x2+6x+9 then form a polynomial whose zeroes are -alpha and -beta

Answer 1

Hi Mate !!

Given equation :- x² + 6x + 9

Let's factorise it by middle term splitting :- x² + 6x + 9

x² + 3x + 3x + 9

x ( x + 3 ) + 3 ( x + 3 )

( x + 3 ) ( x + 3 )

• ( x + 3 ) = 0

x = ( - 3 )

• ( x + 3 ) = 0

x = ( - 3 )

$so \: \: \: \alpha \: \: and \: \: \beta \: \: are \: \: ( - 3) \: \: respectively$



• The new equation having Zeros as :-

$- \alpha \: \: \: \: and \: \: \: \: \: - \beta$


$- \alpha = - ( - 3) = 3$


$- \beta = - ( - 3) = 3$


So, the Zeros are 3

• Sum of the Zeros are :-

3 + 3 = 6

• Product of the Zeros are :-

3 × 3 = 9


♯ To form the quadratic equation we have formula as :-

x² - ( sum of Zeros )x + ( product of Zeros)

Putting value in it !!

x² - 6x + 9 is the required quadratic equation !!

Answer 2

Answer:

Step-by-step explanation: