The polynomial 3x^2-2x-2 has roots p,q. what is the value of 1/p + 1/q?
To find the value of 1/p + 1/q, we need to determine the values of p and q, which are the roots of the polynomial 3x^2 - 2x - 2.
Step 1: Recall that the sum of the roots of a quadratic equation of the form ax^2 + bx + c = 0 is equal to -b/a.
In this case, the sum of the roots p and q is given by:
Sum of the roots = -(coefficient of x) / (coefficient of x^2) = -(-2) / 3 = 2/3.
Step 2: Recall that the product of the roots of a quadratic equation of the form ax^2 + bx + c = 0 is equal to c/a.
In this case, the product of the roots p and q is given by:
Product of the roots = (constant term) / (coefficient of x^2) = -2 / 3 = -2/3.
Step 3: Now, we can use the sum and product of the roots to find the value of 1/p + 1/q.
Since 1/p + 1/q = (p + q) / (pq), we can substitute the values:
1/p + 1/q = (2/3) / (-2/3).
To simplify this expression, we can multiply the numerator and denominator by the reciprocal of -2/3, which is -3/2:
1/p + 1/q = (2/3) / (-2/3) * (-3/2) = (2/3) * (-3/2) / (-2/3) = -1.
Therefore, the value of 1/p + 1/q is -1.