Question

разложите на множители квадратный трехчлен :
а) х^-15x+26 б)4y^+3y-7

Answer 1

$a)\\x^{2}-15x+26=0\\x_{1}=frac{-b-sqrt{b^{2}-4ac}}{2a}=frac{15-sqrt{15^{2}-4*1*26}}{2*1}=frac{15-sqrt{121}}{2}=frac{15-11}{2}=2\\x_{2}=frac{-b+sqrt{b^{2}-4ac}}{2a}=frac{15+sqrt{15^{2}-4*1*26}}{2*1}=frac{15+sqrt{121}}{2}=frac{15+11}{2}=13\\ax^{2}+bx+c=a*(x-x_{1})(x-x_{2})\\x^{2}-15x+26=(x-2)(x-13)\\b)\\4y^{2}+3y-7=0\\x_{1}=frac{-b-sqrt{b^{2}-4ac}}{2a}=frac{-3-sqrt{3^{2}-4*4*(-7)}}{2*4}=frac{-3-sqrt{121}}{8}=frac{-3-11}{8}=-frac{7}{4}$

$x_{2}=frac{-b+sqrt{b^{2}-4ac}}{2a}=frac{-3+sqrt{3^{2}-4*4*(-7)}}{2*4}=frac{-3+sqrt{121}}{8}=frac{-3+11}{8}=1\\ax^{2}+bx+c=a*(x-x_{1})(x-x_{2})\\4y^{2}+3y-7=4*(x+frac{7}{4})(x-1)=(4x+7)(x-1)$