Answer:
Explanation:
f(x)=3x
2
+9x−16
Quadratic polynomial can be factored using the transformation ax
2
+bx+c=a(x−x
1
)(x−x
2
), where x
1
and x
2
are the solutions of the quadratic equation ax
2
+bx+c=0.
3x
2
+9x−16=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=
2×3
−9±
9
2
−4×3(−16)
Square 9.
x=
2×3
−9±
81−4×3(−16)
Multiply −4 times 3.
x=
2×3
−9±
81−12(−16)
Multiply −12 times −16.
x=
2×3
−9±
81+192
Add 81 to 192.
x=
2×3
−9±
273
Multiply 2 times 3.
x=
6
−9±
273
Now solve the equation x=
6
−9±
273
when ± is plus. Add −9 to
273
.
x=
6
273
−9
Divide −9+
273
by 6.
x=
6
273
−
2
3
Now solve the equation x=
6
−9±
273
when ± is minus. Subtract
273
from −9.