Question

If a and b are zeroes of x^2-7x+12

Answer 1

$\tt\sf\rightarrow \: \alpha \: and \: \beta \: are \: zeros \: of \: polynomial \\ \\\tt\sf\rightarrow {x}^{2} - 7 \: x + 12 \\ \\ \\ \tt\sf\rightarrow \alpha \beta = 12 \: the \: product \: of \: the \: roots \: is \: the \\ \tt\sf \: \: constant \: term \: \\ \\ \tt\sf\rightarrow \: \alpha + \beta + 7 \: the \: sum \: of \: the \: roots \: is \: the \\ \tt\sf \: coefficient \: of \: x \: term \: \\ \\ \tt\sf\rightarrow \: \frac{1}{ \alpha } + \frac{1}{ \beta } + 2 \alpha \beta \\ \\ \tt\sf\rightarrow \frac{( \alpha + \beta )}{a \ \: \beta } + 2 \alpha \beta \\ \\ \tt\sf\rightarrow \frac{12}{7} + 2 \times 12 \\ \\ \tt\sf\rightarrow24 + \frac{12}{7} \\ \\ \tt\sf\rightarrow \frac{180}{7}$