Question

What are the zeros of the parabola: f(x) = x2 - 7x + 10 (that is, what are the x-intercepts or the points where the graph crosses the x-axis)?

Answer 1

Answer:

$x=2\ or\ x=5\Rightarrow(2,\ 0)\ \vee\ (5,\ 0)$

Step-by-step explanation:

$f(x)=x^2-7x+10\\\\\text{The zeros of the parabola}\ f(x):\\\\f(x)=0\to x^2-7x+10=0\\\\\left\begin{array}{ccc}a+b=-7\\\\ab=10\end{array}\right\}\Rightarrow a=-2,\ b=-5\\\\x^2-2x-5x+10=0\qquad\text{use the distributive property}\\\\x(x-2)-5(x-2)=0\\\\(x-2)(x-5)=0\iff x-2=0\ \vee\ x-5=0\\\\x-2=0\qquad\text{add 2 to both sides}\\x-2+2=0+2\\\boxed{x=2}\\\\x-5=0\qquad\text{add 5 to both sides}\\x-5+5=0+5\\\boxed{x=5}$

Answer 2

Answer:

5 and -5

Step-by-step explanation: