Question

if the zeros of the quadratic polynomial x2
+ (A + 1) X + B are 2 and 3 then find the value of a and b

Answer 1

$put \: x = 2 \\ {x}^{2} + (a + 1)x + b = 0 \\ {2}^{2} + (a + 1) \times 2 + b = 0 \\ 4 + 2a + 2 + b = 0 \\ 2a + b = - 6 \: \: \: \: \: \: \: eq1\\ \\ put \: x = 3 \\ {3}^{2} + (a + 1)3 + b = 0 \\ 9 + 3a + 3 + b = 0 \\ 3a + b = - 12 \: \: \: \: \: eq2 \: \: \\ subtract \: both \: equations \\ - a = 6 \\ a = - 6 \: \: \: \: \: ans \\ 2( - 6) + b = - 6 \\ - 12 + b = - 6 \\ b = - 6 + 12 \\ b = 6 \: \: \: \: ans$