Answer :
Answer:
- a = 0
- b = -6
Step-by-step explanation:
We can the value of a and b by using the factor theorem, where:
"If a is a zero of a polynomial f(x), then one of its factors is (x - a) and f(a) = 0"
Given that the zeros for f(x) = x² + (a + 1)x + b are 2 and -3, then:
- f(2) = 0
- f(3) = 0
for f(2) = 0:
[tex]f(2)=0[/tex]
[tex]2^2+(a+1)(2)+b=0[/tex]
[tex]4+2a+2+b=0[/tex]
[tex]2a+b=-6\ \text{ ... [1]}[/tex]
for f(-3) = 0:
[tex]f(-3)=0[/tex]
[tex](-3)^2+(a+1)(-3)+b=0[/tex]
[tex]9-3a-3+b=0[/tex]
[tex]-3a+b=-6\ \text{ ... [2]}[/tex]
Combining [1] & [2]:
[tex]\begin{aligned}\\2a+b&=-6\\-3a+b&=-6\\-----&----\ (-)\\5a&=0\\\bf a&=0\end{aligned}[/tex]
Substitute a = 0 into [1]
[tex]2a+b=-6[/tex]
[tex]2(0)+b=-6[/tex]
[tex]\bf b=-6[/tex]
