To find α² + β², we can use the relationship between the roots and coefficients of a quadratic equation.

The sum of the roots (α + β) is given by -b/a, and the product of the roots (αβ) is given by c/a, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = 5, and c = -2.

So, α + β = -b/a = -5/3 and αβ = c/a = -2/3.

We know that α² + β² = (α + β)² - 2αβ.

Substituting the values we found for α + β and αβ:

α² + β² = (-5/3)² - 2*(-2/3) = 25/9 + 4/3 = 25/9 + 12/9 = 37/9.

So, α² + β² = 37/9.

Question

To find α² + β², we can use the relationship between the roots and coefficients of a quadratic equation.

The sum of the roots (α + β) is given by -b/a, and the product of the roots (αβ) is given by c/a, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = 5, and c = -2.

So, α + β = -b/a = -5/3 and αβ = c/a = -2/3.

We know that α² + β² = (α + β)² - 2αβ.

Substituting the values we found for α + β and αβ:

α² + β² = (-5/3)² - 2*(-2/3) = 25/9 + 4/3 = 25/9 + 12/9 = 37/9.

So, α² + β² = 37/9.

Knowee AI · Accepted Answer

To find α² + β², we can use the relationship between the roots and coefficients of a quadratic equation.

The sum of the roots (α + β) is given by -b/a, and the product of the roots (αβ) is given by c/a, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = 5, and c = -2.

So, α + β = -b/a = -5/3 and αβ = c/a = -2/3.

We know that α² + β² = (α + β)² - 2αβ.

Substituting the values we found for α + β and αβ:

α² + β² = (-5/3)² - 2*(-2/3) = 25/9 + 4/3 = 25/9 + 12/9 = 37/9.

So, α² + β² = 37/9.

If α and β are the roots of the equation 3x2 + 5x − 2 = 0, what is α2 + β2

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