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Vieta's formula relates the coefficients of polynomials to the sum and products of their roots. This can provide a shortcut to finding solutions in more complicated algebraic polynomials.
What is the product of roots of the quadratic equation
\[2 x^2 - 6 x + 36 = 0, \]
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If the two roots of the quadratic equation \(x^2-12x-2=0\) are \(\alpha\) and \(\beta\), what is \(\alpha^2+\beta^2\)?
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The difference between the two roots of the quadratic equation \[x^2+Ax+B=0\] is \(12\) and the larger root is \(3\) times the smaller root. What is the value of \(A+B\)?
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What are the sum of roots of the quadratic equation
\[ x^2 - 9 x + 15 = 0?\]
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Let \(\alpha\) and \(\beta\) be the two roots of the quadratic equation \[x^2-16x+63=0.\] What is the value of \(\alpha+\beta+\alpha\beta\)?
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