Sum and product of roots, hidden quadratics, line meets parabola
Read the sum and product of the roots from the coefficients, solve an x to the fourth equation by a change of letter, and find where a line meets a parabola.
- سوريا: الصف ١٠
- فلسطين: الصف ١١
- إيران: الصف ١١
- أوكرانيا: الصف ٨
- روسيا: الصف ٨
- ألمانيا: الصف ٩
- فرنسا: الصف ١١
- بريطانيا: السنة ١١
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
If x٢ + bx + c = ٠ has roots r and s, then (x − r)(x − s) = x٢ − (r + s)x + rs. So the roots add to r + s = −b and multiply to rs = c. For ax٢ + bx + c = ٠: sum −b ÷ a, product c ÷ a. You can read these without finding the roots.
Some equations are not quadratics but turn into one. In x٤ − ٥x٢ + ٤ = ٠ let u = x٢; then u٢ − ٥u + ٤ = ٠. Solve for u first, then use x٢ = u to find x.
A line and a parabola meet where their y values are equal. Set the two expressions for y equal; you get a quadratic, and each root of it is the x of a meeting point.
In each task, mark the roots or x values with points on the number line.