Answer:
a) The equation in intercept form by factoring is (x+6)(x+4)
b) From the given graph x- intercepts are (-4,0) and (-6,0) and zeros (roots) of the function are -6 and -4.
c) The solutions of [tex]2x^2+20x+48=0[/tex] is [tex](x+6)(x+4)=0[/tex] that is x= -6 and x = -4.
Step-by-step explanation:
The given quadratic equation is [tex]f(x)=2x^2+20x+48[/tex]
Put the function f(x) = 0 , then [tex]f(x)=2x^2+20x+48=0[/tex]
a) The equation in intercept form by factoring is ,
Consider the given function,
[tex]f(x)=2x^2+20x+48=0[/tex]
[tex]\Rightarrow 2x^2+20x+48=0[/tex]
taking 2 common, we get,
[tex]\Rightarrow 2(x^2+10x+24)=0[/tex]
[tex]\Rightarrow x^2+10x+24=0[/tex]
The above is a quadratic equation of the form [tex]ax^2+bx+c=0[/tex]
Solving quadratic equation using middle term splitting method,
[tex]\Rightarrow x^2+6x+4x+24=0[/tex]
[tex]\Rightarrow x(x+6)+4(x+6)=0[/tex]
[tex]\Rightarrow (x+6)(x+4)=0[/tex]
Thus, The equation in intercept form by factoring is (x+6)(x+4).
b) From the given graph x- intercepts are (-4,0) and (-6,0) .
Zeroes / roots of a function are those points where the value of the function is zero.
Put f(x) = 0 as solved above
that is [tex] (x+6)(x+4)=0[/tex]
[tex]\Rightarrow (x+6)=0[/tex] or [tex]\Rightarrow (x+4)=0[/tex]
[tex]\Rightarrow x=-6[/tex] or [tex]\Rightarrow x=-4[/tex]
Thus, zeros (roots) of the function are -6 and -4.
For checking put x = -6 and -4 in the function we get f(x) =0 .
c) The solutions of [tex]2x^2+20x+48=0[/tex] is [tex](x+6)(x+4)=0[/tex] that is x= -6 and x = -4 as shown above.
