Question

The roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?

x = –1 and x =__

Answer 1

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Answer 2

Answer: The required number is 3.

Step-by-step explanation: Given that the roots of the function
`f(x)=x^2-2x-3` are shown below :

`x=-1,x=?`

We are to find the missing number.

To find the missing number, we must solve the quadratic equation f(x) = 0.

We have

`f(x)=0\\\\\Rightarrow x^2-2x-3=0\\\\\Rightarrow x^2-3x+x-3=0\\\\\Rightarrow x(x-3)+1(x-3)=0\\\\\Rightarrow (x+1)(x-3)=0\\\\\Rightarrow x+1=0,x-3=0\\\\\Rightarrow x=-1,3.`

Therefore, the roots of the given equation are x = -1 and x = 3.

Thus, the required number is 3.