Let the quadratic equation be \( ax^2 + bx + c = 0 ; a ≠ 0. \)

Let the quadratic polynomial \( ax^2 + bx + c \) be expressible as the product of two linear factors, say (px + q) and (rx + s), where p. q, r, s are real numbers such that p ≠ 0 and r ≠ 0. Then,

Solving these linear equations, we get the possible roots of the given quadratic equation as

\( x = -p/q and x = s/r \)**Example **: \( x^2+6x+5 = 0 \)

We have,

\( x^2+ 6x +5=0 \) \( x^2+ 5x+ x÷5= 0 \) \( x (x+5)+ (x+5) = 0 \) \( (x+5) (x+1) = 0 \)\( x+5= 0 or, x +1- 0 \)

\( x= -5 or x = -1 \)

Thus, x = -5 and x = – 1 are two roots of the equation \( x^2 + 6x +5 = 0 \)