Question

Write a quadratic function h whose only zero is 1

Answer 1

x^2-2x+1

this factors out to (x-1)(x-)

both of those are equal to x=1

Answer 2

`x^(2)-2x+1`

Explanation:

1)A quadratic function with only one zero, i.e. root, must have its Δ =0.
`\Delta =b^(2)-4ac`

2)
`x^(2)-2x+1`

3) Solving by the Quadratic Formula:

`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}=(-(-2)\pm √(4-4(1)(1)))/(2(1))=(2\pm √(0))/(2)=1 \Rightarrow S=\left \{ 1 \right \}`

4) Alternatively, solving by factoring:

`x^(2)-2x+1=(x-1)^2=(x-1)(x-1)\Rightarrow S=\left \{ 1 \right \}`

For 1 - 1 is equal to zero.