Find the Sum and Product of Roots of the Polynomial 2x²+x-5=0

Find the Sum and Product of Roots of the Polynomial 2x²+x-5=0

Solution:

To find the sum and product of the roots of the polynomial 2x² + x – 5 = 0, we can use the relations between the coefficients and the roots of a quadratic equation.

The given quadratic equation is in the form of ax² + bx + c = 0, where a = 2, b = 1, and c = -5.

The sum of the roots (α + β) can be found using the formula: α + β = -b/a.

Substituting the values into the formula, we have: α + β = -(1)/(2) = -1/2.

The product of the roots (αβ) can be found using the formula: αβ = c/a.

Substituting the values into the formula, we have: αβ = (-5)/(2) = -5/2.

Therefore, the sum of the roots is -1/2 and the product of the roots is -5/2.

Answer:

The Sum and Product of Roots of the Polynomial 2x²+x-5=0 is α+ β = -1/2 and αβ = -5/2

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