Question

Solve equation 2x^{2}−5x−7 = 0 by using the quadratic formula. Then write 2x^{2}−5x−7 in form of a(x−r_{1})(x−r_{2}).

Answer 1

`2x^2+2x-7x-7=2x(x+1)-7(x+1)=(2x-7)(x+1)=\\ \\=2(x-3.5)(x+1)\\ \\2x^2-5x-7=0\ \ \ \Leftrightarrow\ \ \ 2(x-3.5)(x+1)=0\\ \\x-3.5=0\ \ \vee\ \ \ x+1=0\\ \\.\ \ \ \ \ \ \ x=3.5\ \ \ \ \ \ \ \ \ \ \ x=-1`