If α and β are the Zeros of the Quadratic Polynomial p(y) = 5y² -7y + 1, Find the Value of 1/α+1/β
By BYJU'S Exam Prep
Updated on: October 17th, 2023
If α and β are the zeros of the quadratic polynomial p(y) = 5y² -7y + 1, find the value of 1/α+1/β
Let us see the steps to find out the value of 1/α+1/β.
Step 1: Identify the coefficients of the polynomial: a = 5, b = -7, and c = 1.
Step 2: Use sum of zeros and producr of zeros to find the zeros of the polynomial
Step 3: Identify the values of α and β and then find the value of 1/α + 1/β
Step 4: Simplify the expression to find the numerator and the denominator
Table of content
If α and β are the Zeros of the Quadratic Polynomial p(y) = 5y² -7y + 1, Find the Value of 1/α+1/β
Solution:
To find the value of 1/α + 1/β, where α and β are the zeros of the quadratic polynomial p(y) = 5y² – 7y + 1, we need to determine the values of α and β first.
We know that the sum of the zeros of a quadratic polynomial can be found using the formula:
α + β = -b/a,
where a and b are the coefficients of the polynomial.
In this case, the coefficient of y² is 5 (a) and the coefficient of y is -7 (b). Therefore:
α + β = -(-7)/5 = 7/5.
Next, we’ll find the product of the zeros of the polynomial using the formula:
α × β = c/a,
where c is the constant term and a is the coefficient of y².
In this case, the constant term is 1 and the coefficient of y² is 5. Therefore:
α × β = 1/5.
Now, we can calculate the value of 1/α + 1/β using the values of α and β:
1/α + 1/β = (α + β)/(α × β) = (7/5)/(1/5) = 7.
Hence, the value of 1/α + 1/β is 7.
Answer:
If α and β are the Zeros of the Quadratic Polynomial p(y) = 5y² -7y + 1, the Value of 1/α+1/β is 7
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