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Answer:

The equation which has ONLY two solution x = 3 and x = -3 is [tex]P(x)  = x^2 - 9[/tex]

Step-by-step explanation:

Here, the ONLY two rrots of the equation is given as:

x =  3 and x = -3

Now, if x = a is the ZERO of the polynomial, then x  - a  = 0 is the ROOT of the polynomial.

So, here the only roots of the polynomial are : (x-3) and (x+3)

Also, the POLYNOMIAL = PRODUCT OF ALL ROOTS

So, [tex]P(x) = (x-3)(x+3)    = x(x+3) -3(x+3)  = x^2 + 3x - 3x - 9  = x^2 - 9\\\implies P(x)  = x^2 - 9[/tex]

Hence, the equation which has ONLY two solution x = 3 and x = -3 is [tex]P(x)  = x^2 - 9[/tex]

The equation has only two solution x = 3 and x = -3 is [tex]x^2-9[/tex].

We have to determine, the equation which has only two solutions x  = 3 and x = -3.

According to the question,

The two roots of the equation is x = 3 and x = -3,

if x = a is the zero of the polynomial, then x - a  = 0 is the root of the polynomial.

So, here the only roots of the polynomial are : (x-3) and (x+3).

If the [tex]\alpha[/tex] and [tex]\beta[/tex] are the roots of the equation the product of roots can be written as,

[tex]Product \ of \ roots = \alpha \times \beta[/tex]

Substitute the values in the equation,

[tex]= (x-3 ) (x+3)\\\\= x (x+3) - 3(x+3)\\\\= x^2 + 3x -3x -9\\\\= x^2 - 9[/tex]

Hence, The required equation has only two solution x = 3 and x = -3 is [tex]x^2-9[/tex].

To know more about Quadratic Equations click the link given below.

https://brainly.com/question/437300

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