Question

Find the least positive value of a for which the equation ax^2 -4x + 9= 0 has integral roots​

Answer 1

Step-by-step explanation:

$Given \: quadratic \: equation \: is : \\ \: \: \: \: \: \: \: \: \: \: \: \: a {x}^{2} - 4x + 9 = 0 \\ \implies \: a {x}^{2} + bx + c = 0 \: \\ here \\ a = a \\ b - 4 \\ c = 9 \\ \because \:Given \: quadratic \: equation \: has \: \\ integral \: roots \\ \therefore \: \: \: {b}^{2} - 4ac = 0 \\ \implies \: {( - 4)}^{2} - 4a \times 9 = 0\\ \implies \: 16 - 36a= 0\\ \implies \: 16 = 36a \\ \implies \: a = \frac{16}{36} \\ \implies \: a = \frac{4}{9}$