If the Squared Difference of the Zeros of Polynomial x2+px+45 is 144 Then Find p
By BYJU'S Exam Prep
Updated on: October 17th, 2023
If the squared difference of the zeros of polynomial x2+px+45 is 144 then find p.
Steps to find the value of p are:
- Let α and β be the zeros of the polynomial x2+ px + 45 = 0 and squared difference of the zeros is given as (α – β)2 = 144.
- Expand the squared difference.
- Then use α + β = -p, and the product of the zeros is αβ = 45.
- Substitute these values into the equation: (α2 – 2αβ + β2) and simplify the equation to get the result.
Table of content
If the Squared Difference of the Zeros of Polynomial x2+px+45 is 144 Then Find p
Given the polynomial x^2 + px + 45, and the squared difference of the zeros is 144.
We know that the squared difference of the zeros (α – β)^2 is equal to (α + β)^2 – 4αβ.
Using the formula for the sum of the zeros (α + β) and the product of the zeros αβ, we have:
(α – β)^2 = (α + β)^2 – 4αβ
Substituting the values into the equation, we get:
144 = (-p)^2 – 4(45)
Simplifying further:
144 = p^2 – 180
Rearranging the equation:
p^2 = 324
Taking the square root of both sides:
p = ±√324
p = ±18
Therefore, the value of p can be either 18 or -18, depending on the positive or negative square root.
Hence, the possible values of p are 18 and -18.
Answer
The value of p are 18 and -18.
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