Quadratic inequalities and parameters
Solve quadratic inequalities by the signs of their factors, and see how a letter in an equation turns 'how many roots?' into an inequality.
- سوريا: الصف ١٠
- فلسطين: الصف ١٠
- إيران: الصف ١٠
- أفغانستان: الصف ٩
- أوكرانيا: الصف ٩
- روسيا: الصف ٩
- بريطانيا: السنة ١٠
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
This workshop follows 'signs of products'. Here a quadratic such as x٢ − ٤ is first split into factors: (x − ٢)(x + ٢).
A product of two factors is negative when the factors have opposite signs. The zeros of the factors cut the line into gaps; in each gap write the sign of each factor, and get the sign of the product from the rule of signs.
A square is never negative: (x − ١)٢ ≥ ٠. So in (x − ١)٢ > ٠ only the one point x = ١ fails.
Sometimes an equation has another letter in it, such as a in x٢ + ax + ١ = ٠. The المميز Δ = a٢ − ٤ tells you how many roots there are. Two roots means Δ > ٠, which is itself a quadratic inequality, but now in the letter a.
Tap the line to get a piece, choose its shape with the buttons, and tap a dot to make it filled or hollow. Under the line the answer is written as an inequality and in interval notation.