Find the Zeroes of the Polynomial x^2 + x – p(p+1)
By BYJU'S Exam Prep
Updated on: October 17th, 2023
x = p and x = -1 – p are the zeros of the polynomial.
To solve the given polynomial, we will use the following steps:
- Apply the quadratic formula: x = (-b ± √(b^2 – 4ac)) / (2a).
- Substitute the values of a, b, and c into the quadratic formula and simplify.
- Split the equation into two separate equations and find out two duifferent roots/zeros of the polynomial.
Table of content
Find the Zeroes of the Polynomial x^2 + x – p(p+1)
Solution:
Let’s go through a more detailed solution to find the zeros of the polynomial x^2 + x – p(p+1).
To find the zeroes, we set the polynomial equal to zero:
x^2 + x – p(p+1) = 0
Now, we’ll use the quadratic formula to solve for x:
x = (-b ± √(b^2 – 4ac)) / (2a)
Comparing our equation to the standard form ax^2 + bx + c = 0,
we have:
a = 1
b = 1
c = -p(p+1)
Substituting these values into the quadratic formula, we get:
x = (-(1) ± √[(1)^2 – 4(1)(-p(p+1)))] / (2(1))
x = (-1 ± √(1 + 4p(p+1))) / 2
x = (-1 ± √(1 + 4p^2 + 4p)) / 2
x = (-1 ± √(4p^2 + 4p + 1)) / 2
Simplifying further, we have:
x = (-1 ± √((2p + 1)^2)) / 2
x = (-1 ± (2p + 1)) / 2
Now, we can split this equation into two separate equations:
x = (-1 + (2p + 1)) / 2x
= (2p) / 2
x = p
x = (-1 – (2p + 1)) / 2
x = (-2 – 2p) / 2
x = -1 – p
Therefore, the zeros of the polynomial x^2 + x – p(p+1) are x = p and x = -1 – p.
Answer:
Zeros of the Polynomial x^2 + x – p(p+1)
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