# 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

By BYJU'S Exam Prep

Updated on: October 17th, 2023

If the zeroes of the polynomial x²+px+q are double in value to the zeroes of 2x²-5x -3, find the value of p and q

Here are the steps in brief to find the values of p and q:

Step 1: Set the zeros of the polynomial x² + px + q as α and β.

Step 2: Express the relationship between the zeros of 2x² – 5x – 3 and x² + px + q as α = 2α’ and β = 2β’, where α’ and β’ are the zeros of 2x² – 5x – 3.

Step 3: Find the zeros of 2x² – 5x – 3 by factoring or using the quadratic formula. In this case, we have x = -1/2 and x = 3 as the zeros.

Step 4: Multiply the zeros of 2x² – 5x – 3 by 2 to obtain the values of α and β. This gives α = -1 and β = 6.

Step 5: The value of p is the sum of the zeros, p = α + β and the value of q is the product of the zeros, q = α * β

## 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.