Question

Which equation has only two solution x=3 and x=-3

Answer 1

Answer:

The equation which has ONLY two solution x = 3 and x = -3 is $P(x) = x^2 - 9$

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, $P(x) = (x-3)(x+3) = x(x+3) -3(x+3) = x^2 + 3x - 3x - 9 = x^2 - 9\\\implies P(x) = x^2 - 9$

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