If α and β are the zeros of the quadratic polynomial f(x) = x2 − x − 4, find the value of 1/α + 1/β – αβ.
By BYJU'S Exam Prep
Updated on: October 17th, 2023
If α and β are the zeros of the quadratic polynomial f(x) = x2 − x − 4, the value of 1/α + 1/β – αβ is 15/4. Before attempting to solve them, candidates should write polynomial equations in standard form. Factor it, and when all the variable factors have reached zero, set them all to zero. The answers to the derived equations are the solutions to the original equations.
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f(x) = x2 − x − 4, find the value of 1/α + 1/β – αβ.
The only operations used in a polynomial are addition, subtraction, multiplication, and positive-integer powers of the variables. It consists of coefficients and indeterminates, commonly known as variables. The question states “If α and β are the zeros of the quadratic polynomial f(x) = x2 − x − 4, find the value of 1/α + 1/β – αβ.”
A polynomial function can only have real roots that are almost equal to its degree. Find a function’s roots by setting the value of the function to zero. Here are the steps for finding the value of 1/α + 1/β – αβ:
Given, f(x) = x2−x−4
Sum of zeros = α+β = 1
Product of zeros = αβ = −4
Now, 1/α + 1/β – αβ
= {(α+β)/αβ} – αβ
= (1/-4) – (-4)
= 15/4
Hence, if α and β are the zeros of the quadratic polynomial f(x) = x2−x−4, the value of 1/α+1/β-αβ is 15/4.
Summary:
If α and β are the zeros of the quadratic polynomial f(x) = x2 − x − 4, find the value of 1/α + 1/β – αβ.
The value of 1/α + 1/β – αβ is 15/4 if α and β are the zeros of the quadratic polynomial f(x) = x2 − x − 4. The sum of zeros is equal to b/a, and the product of zeros is equal to c/a. The equation k [x2 – (zero-sum)x + (zero product)] denotes a quadratic polynomial. Candidates should write polynomial equations in standard form before attempting to solve them. Calculate the factors and then set each variable factor to zero once they have all reached zero.
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