x – x + = . This also means that is a zero of the quadratic polynomial x – x + . In general, a real number is called a root of the quadratic equation ax + bx + c = , a if a + b + c = . We also say that x = is a solution of the quadratic equation , or that satisfies the quadratic equation .
Note that the zeroes of the quadratic polynomial ax + bx + c and the roots of the quadratic equation ax + bx + c = are the same . You have observed, in Chapter , that a quadratic polynomial can have at most two zeroes. So, any quadratic equation can have atmost two roots. You have learnt in Class IX, how to factorise quadratic polynomials by splitting their middle terms.
We shall use this knowledge for finding the roots of a quadratic equation. Let us see how. Example : Find the roots of the equation x – x + = , by factorisation. Solution : Let us first split the middle term – x as – x – x [because (– x ) × (– x ) = x = ( x ) × ].
x – x + = x – x – x + = x ( x – ) – ( x – ) = ( x – )( x – ) Now, x – x + = can be rewritten as ( x – )( x – ) = . So, the values of x for which x – x + = are the same for which ( x – )( x – ) = , i.e., either x – = or x – = . Now, x –