Question

If are the zeros of the polynomial: x^2 + 6x + 9, then form a polynomial whose zeros are :
(a) − − (b) 2 2
Please do it without finding the zeroes of the polynomial. Thanks.

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 )

$\text{ so Alpha and beta are ( - 3) respectively }$

• The new equation having Zeros as :-

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

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

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

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:

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 )

• The new equation having Zeros as :-

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!!

Step-by-step explanation: