Question

What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9? x = –4 – and x = –4 + x = –4 – and x = –4 + x = –4 – and x = –4 + x = –4 – and x = –4 +

Answer 1

$\text{The zeros of the function:}\ f(x)=0\\\\f(x)=2x^2+16x-9\to2x^2+16x-9=0\ \ \ \ |+9\\\\2x^2+16x=9\ \ \ |:2\\\\x^2+8x=4.5\\\\x^2+2x\cdot4=4.5\ \ \ |+4^2\\\\\underbrace{x^2+2x\cdot4+4^2}_{(a+b)^2=a^2+2ab+b^2}=4.5+4^2\\\\(x+4)^2=20.5\iff x+4=\pm\sqrt{20.5}\ \ \ \ |-4\\\\x=-\sqrt{20.5}-4\ \vee\ x=\sqrt{20.5}-4$