Question

What are the zeros of the quadratic function f(x) = 2x2 + 8x – 3? x = –2 – and x = –2 + x = –2 – and x = –2 + x = 2 – and x = 2 + x = 2 – and x = 2 +

Answer 1

`\text{The zeros of the function:}\ f(x)=0\\\\f(x)=2x^2+8x-3\to2x^2+8x-3=0\ \ \ |+3\\\\2x^2+8x=3\ \ \ |:2\\\\x^2+4x=1.5\\\\x^2+2x\cdot2=1.5\ \ \ \ |+2^2\\\\\underbrace{x^2+2x\cdot2+2^2}_((a+b)^2=a^2+2ab+b^2)=1.5+2^2\\\\(x+2)^2=5.5\to x+6=\pm√(5.5)\ \ \ \ |-6\\\\x=-√(5.5)-6\ \vee\ x=√(5.5)-6`