For every MCQ the correct alternative. a, b, cord of answer with sub nswer. For which of the following equations has \( \alpha+\beta=14 \) and \( \alpha \times \beta=33 \) ? \( \begin{array}{llll}\text { a) } x^{2}-14 x+33=0 & \text { b) } x^{2}+8 x+33=0 & \text { c) } x^{2}-14 x-33=0 & \text { d) } x^{2}+14 x-33 \\ \text { Which number cannot represent the probability? }\end{array} \)

The correct alternative for the first question is: a) \( x^{2}-14 x+33=0 \). This is because the equations formed by the roots \( \alpha \) and \( \beta \) are based on Vieta's formulas, which state that for a quadratic equation \( x^2 - (sum) x + (product) = 0 \). Here, since \( \alpha+\beta=14 \) and \( \alpha \times \beta=33 \), it matches option 'a'. For the second question about which number cannot represent probability, remember that probabilities must always be between 0 and 1, inclusive. Therefore, any number outside of this range (like -1 or 2, for example) cannot represent a probability! It’s a great way to remember to keep your limits in check when dealing with probabilities!