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Given the roots of the equation 3x2 − 4x + 2 = 0 are alpha and beta. Find the sum and product of the roots.

Mathematics

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1. Given the roots of the equation 3x2−4x+2=03x^2 - 4x + 2 = 0 are α\alpha and β\beta.

For a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0:
Sum of roots: α+β=−ba\alpha + \beta = -\frac{b}{a}
Product of roots: αβ=ca\alpha\beta = \frac{c}{a}

For 3x2−4x+2=03x^2 - 4x + 2 = 0, we have a=3a=3, b=−4b=-4, c=2c=2.

α+β=−−43=43\alpha + \beta = -\frac{-4}{3} = \frac{4}{3}
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