Question

For the quadratic equation \[ ax^{2} + bx + c = 0 \], the middle-term numbers chosen by splitting must satisfy which condition?

Options

• Their sum is \( c \).

• Their sum is \( b \).

• Their sum is \( a \).

• Their sum is \( a \times c \).

Answer 1

For splitting the middle term of \[ ax^{2} + bx + c = 0 \], the product of middle-term numbers is \[ a \times c \] and the sum of middle-term numbers is \( b \). The sum condition ensures the split terms recombine to the original middle term \( bx \).