Разложение квадратного трехчлена на множители
Каждый квадратный трехчлен ax 2 + bx+ c может быть разложен на множители первой степени следующим образом.
Решим квадратное уравнение:
ax 2 + bx+ c = 0
Если x1 и x2 - корни этого уравнения, то
ax 2 + bx+ c = a ( x – x1 ) ( x – x2 ) .
Это можно доказать, используя либо формулы корней неприведенного квадратного уравнения, либо теорему Виета.
Пример: Разложить трехчлен 2x 2 – 4x – 6 на множители первой степени.
Решение Во-первых, решим уравнение: 2x 2 – 4x – 6 = 0. Его корни:
x1 = –1 и x2 = 3. Отсюда, 2x 2 – 4x – 6 = 2 ( x + 1 ) ( x – 3 ) .
Вопросы к конспектам
Сократить дробь: ![begin mathsize 12px style fraction numerator a squared minus 25 over denominator 3 a plus 15 end fraction end 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Сократить дробь:
Сократить дробь: ![begin mathsize 12px style fraction numerator 5 x squared plus x minus 4 over denominator x squared plus x end fraction end 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Какое выражение надо записать вместо (…), чтобы равенство было верным. 2х²-13х+6=(2х-1)(…)
Разложите квадратный трёхчлен на множители: 2x2-7x-15.
Разложите квадратный трёхчлен на множители: 6x2+x-5.
Разложите квадратный трёхчлен на множители: x2+6x-27=0
Разложите квадратный трёхчлен на множители: x2-4x-6.
Разложите квадратный трёхчлен на множители: 5x2-3x-2.
Сократите дробь: ![begin mathsize 12px style fraction numerator a squared minus 9 over denominator 12 a minus 4 a squared end fraction end 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Последнее изменение: Воскресенье, 29 Январь 2017, 19:51