Question

Factor the following and find the zeros.

1. x2 - 169 = 0                2. x2 + 14X + 49 = 0

3. x2 - 17x + 42 = 0        4. 2X2 - 9X - 5 = 0

5. 3X2 + 11X - 4 =0         6. X2 - 169 = 0

Answer 1

`1.\ x^2-169=0\\\\x^2-13^2=0\\\\(x-13)(x+13)=0\iff x=13\ \vee\ x=-13`


`2.\ x^2+14x+49=0\\\\x^2+2x\cdot7+7^2=0\\\\(x+7)^2=0\\\\(x+7)(x+7)=0\iff x=-7`


`3.\ x^2-17x+42=0\\\\x^2-14x-3x+42=0\\\\x(x-14)-3(x-14)=0\\\\(x-14)(x-3)=0\iff x=14\ \vee\ x=3`


`4.\ 2x^2-9x-5=0\\\\2x^2-10x+x-5=0\\\\2x(x-5)+1(x-5)=0\\\\(x-5)(2x+1)=0\iffx=5\ \vee\ x=-(1)/(2)`


`5.\ 3x^2+11x-4=0\\\\3x^2+12x-x-4=0\\\\3x(x+4)-1(x+4)=0\\\\(x+4)(3x-1)=0\iff x=-4\ \vee\ x=(1)/(3)`


`6.\ this\ same\ like\ 1.\\\\x^2-196=0\\\\x^2-14^2=0\\\\(x-14)(x+14)=0\iff x=14\ \vee\ x=-14`