If the Zeros of the Polynomial x²+px+q are Double in Value to the Zeros of 2x²-5x -3, Find the Value of p and q

If the Zeros of the Polynomial x²+px+q are Double in Value to the Zeros of 2x²-5x -3, Find the Value of p and q

Solution:

Let's denote the zeros of the polynomial x² + px + q as α and β.

Given that the zeros of 2x² - 5x - 3 are double in value to the zeros of x² + px + q, we can express this relationship as follows:

α = 2α' β = 2β'

Here, α' and β' represent the zeros of 2x² - 5x - 3.

Now, let's find the zeros of 2x² - 5x - 3. We can either use factoring or the quadratic formula. Using factoring, we have:

2x² - 5x - 3 = (2x + 1)(x - 3)

Setting each factor equal to zero and solving for x, we find the zeros of 2x² - 5x - 3:

2x + 1 = 0

x = -1/2

x - 3 = 0

x = 3

Therefore, the zeros of 2x² - 5x - 3 are x = -1/2 and x = 3.

Since α and β are double the values of α' and β', we can express this relationship as:

α = 2(-1/2) = -1

β = 2(3) = 6

Thus, the value of p is the sum of the zeros: p = α + β = -1 + 6 = 5.

Similarly, the value of q is the product of the zeros: q = α * β = -1 * 6 = -6.

Therefore, the values of p and q are p = 5 and q = -6.

Answer:

If the Zeros of the Polynomial x²+px+q are Double in Value to the Zeros of 2x²-5x -3, then the Value of p and q are 5 and -6

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