Incomplete quadratic equations and the quadratic trinomial
Solve the three kinds of incomplete quadratic equation, find the roots of a quadratic trinomial and factorise it with its leading coefficient.
- Germany: grade 9
- Ukraine: grade 8
- Russia: grade 8
Guide
In the Ukrainian programme this is Grade 8 algebra, §3: item 18 "Quadratic equations. Solving incomplete quadratic equations" and item 21 "The quadratic trinomial".
A quadratic equation ax2 + bx + c = 0 with a ≠ 0 is incomplete if b = 0 or c = 0. There are three kinds. ax2 = 0: the only root is 0. ax2 + bx = 0: factorise x(ax + b) = 0, roots 0 and −ba. ax2 + c = 0: x2 = −ca; if the quotient is positive there are two opposite roots, if negative there are none.
A quadratic trinomial is ax2 + bx + c. A root of the trinomial is a value of x that makes it 0. If p and q are its roots, ax2 + bx + c = a(x − p)(x − q).
Tap a chip, then «Split». Enter roots in the boxes and the factorisation on the keypad.