Given :
Set of x-intercepts {-3,1,7},
point through which it passes (-2,54)
Now,
Step 1: Substitute value of x intercepts in equation, [tex]y=a(x-p)(x-q)(x-r)[/tex], we get,
[tex]y=a(x-(-3))(x-1)(x-7)[/tex]
[tex]y= a(x+3)(x-1)(x-7)[/tex] ... equation (1)
Step 2: substitute x an y with the point through which it passes,
[tex]54=a((-2)+3)((-2)-1)((-2)-7)[/tex]
[tex]54 = 27a[/tex]
∴ [tex]a=2[/tex]
Step 3: Now, substituting value of a in equation (1), we have
[tex]y=(2x+6)(x^{2} -8x+7)[/tex]
[tex]y=2x^{3}-10x^{2} -34x +42[/tex] (Requited cubic equation)
