If alpha and beta are the zeroes of quadratic polynomial 2x²+5x+1 then alpha + beta is?

Question

Answer

Understanding the Quadratic Polynomial
The given quadratic polynomial is:
2x² + 5x + 1
In a quadratic polynomial of the form ax² + bx + c, the sum of the roots (zeroes) can be determined using Vieta's formulas.
Identifying Coefficients
- a = 2 (coefficient of x²)
- b = 5 (coefficient of x)
- c = 1 (constant term)
Using Vieta's Formulas
According to Vieta's formulas, for a quadratic polynomial ax² + bx + c, the sum of the roots (alpha + beta) is given by:
alpha + beta = -b/a
Calculating the Sum of the Roots
Now, substituting the values of b and a:
- b = 5
- a = 2
So,
alpha + beta = -5/2
Final Result
Therefore, the sum of the zeroes (alpha + beta) of the polynomial 2x² + 5x + 1 is:
-2.5 or -5/2
This result clearly shows the relationship between the coefficients of the polynomial and its roots, providing a systematic way to find the sum of the zeroes.

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