# If the Squared Difference of the Zeros of Polynomial x2+px+45 is 144 Then Find p

By Mohit Uniyal|Updated : May 15th, 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.

## 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.

The value of p are 18 and -18.

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