Question

If the product of two zeros of the polynomial f(x)=2x³+6x²-4x+9 is given, what is the value of its third zero? a) 3/2 b) -3/2 c) 9/2 d) -9/2

Answer 1

The value of the third zero of the polynomial f(x)=2x³+6x²-4x+9 is -3/2.

Step-by-step explanation:

To find the value of the third zero of the polynomial, we need to use the fact that the product of the zeros of a polynomial is equal to the constant term divided by the leading coefficient. In this case, the polynomial is f(x) = 2x³ + 6x² - 4x + 9. So the product of the two zeros is 9/2.

To find the third zero, we can use the fact that the sum of the zeros is equal to the opposite of the coefficient of x² divided by the leading coefficient. In this case, the sum of the zeros is -6/2 = -3.

Therefore, the third zero is -3 - (9/2) = -3/2.