Final answer:
The values of p and q for the first polynomial, given that its zeros are double the zeros of the second polynomial 2x² - 5x - 3, are p = -5 and q = -6, respectively.
Step-by-step explanation:
To find the values of p and q given that the zeros of the polynomial x² + px + q are double in value to the zeroes of the polynomial 2x² - 5x - 3, we need to first find the zeros of the second polynomial.
Let's refer to the zeroes of the second polynomial as a and b. Then, the zeroes of the first polynomial will be 2a and 2b because they are double in value. We can use these zeroes to express p and q in terms of a and b.
For the second polynomial, the sum of its roots is -(-5)/2 which equals 5/2, and the product of its roots is -3/2. Therefore, a + b = 5/2 and ab = -3/2.
For the first polynomial, based on the relationship between coefficients and zeros in quadratic equations, we have:
- Sum of roots (2a + 2b) = -p
- Product of roots (2a × 2b) = q
Since the summation and product of the roots of the original polynomial are known, we can deduce:
- p = -2(a + b) = -2(5/2) = -5
- q = 2a × 2b = 4(ab) = 4(-3/2) = -6
Therefore, the values of p and q for the first polynomial are -5 and -6, respectively.