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For the quadratic equation 3x2 − 4x + p = 0, what are the sum and product of its roots in terms of p?

Mathematics

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Step 1: Identify the sum and product of roots for the given equation.
The given quadratic equation is 3x2−4x+p=03x^2 - 4x + p = 0.
For a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0, the sum of the roots is α+β=−ba\alpha + \beta = -\frac{b}{a} and the product of the roots is αβ=ca\alpha\beta = \frac{c}{a}.
In this case, a=3a=3, b=−4b=-4, c=pc=p.
The sum of the roots is:

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

The product of the roots is:

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