f(x)=x²-3x-4 find the roots
Answer (1)
The roots are x = 4 and x = -1.We should find the roots of the following quadratic equation:[tex]\sf f(x)=x^{2} -3x-4[/tex]The roots are the solutions of the quadratic equation. So, we need to solve it. Let's try solving it by factoring.Replace f(x) with y:[tex]\sf y=x^{2} -3x-4[/tex]Replace y with 0:[tex]\sf 0=x^{2} -3x-4[/tex]A factored quadratic equation has this form:[tex]\sf (x+\_\!\_)(x+\_\!\_)=0[/tex]The question is: What do we put in the blanks?Well, what we do is we try to think of two numbers that multiply to -4 and add to -3. These numbers are -4 and 1.So, we write those numbers in the blanks:[tex]\sf (x-4)(x+1)=0[/tex]Now, we set each of these factors equal to 0:[tex]\sf x-4=0 \;or \;x+1=0[/tex]Now, solve each of these equations:[tex]\sf x=4\; or \; x=-1[/tex]
