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.
- أوكرانيا: الصف ٨
- روسيا: الصف ٨
- ألمانيا: الصف ٩
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الدليل
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 ax٢ + bx + c = ٠ with a ≠ ٠ is incomplete if b = 0 or c = 0. There are three kinds. ax٢ = ٠: the only root is 0. ax٢ + bx = ٠: factorise x(ax + b) = ٠, roots 0 and −ba. ax٢ + c = ٠: x٢ = −ca; if the quotient is positive there are two opposite roots, if negative there are none.
A quadratic trinomial is ax٢ + bx + c. A root of the trinomial is a value of x that makes it 0. If p and q are its roots, ax٢ + bx + c = a(x − p)(x − q).
Tap a chip, then «Split». Enter roots in the boxes and the factorisation on the keypad.