how to write a quadratic if the product of the roots is -3?

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We can write a quadratic equation with roots a and b as:

(x - a)(x - b) = 0

=> x^2 - (a+b)x + ab = 0

as the product of the roots is -3.

=> x^2 - ( a + b) - 3 = 0

Now a and b can have several values which satisfy the condition that their product is -3, e.g. (-1 , 3) , ( 3/2 , -2) etc. We are not given any further information about what the roots are.

Therefore the quadratic equation is

x^2 - (a + b) - 3 = 0

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