Question

-3 is a zero of x²+x-6..
State whether it is true or false with reason
And
If x+2 and x-2 are the factors of ax⁴+2x-3x²+bx-4 then the value of a+b is
Plss give answer immediately

Answer 1

Answer:

1) Yes

2) -1

Step-by-step explanation:

1) Applying remainder theorem:

f(x) = x²+x-6

f(-3) = (-3)² + (-3) - 6

f(-3) = 9 - 9 = 0

2)

x-2 = 0 {x = 2}

f(x) = ax⁴+2x-3x²+bx-4

f(2) = 16a+4-12+2b-4

0 = 16a+2b-12

6=8a+b --------------------- 1

x+2 = 0 {x = -2}

f(x) = ax⁴+2x-3x²+bx-4

f(-2) = 16a-4-12-2b-4

0 = 16a-2b-20

10=8a-b --------------------- 2

Adding 1 and 2:

8a+b+8a-b = 6+10

16a = 16 --------------------- a=1

b=6-8a

b=6-8 --------------------- b=(-2)

Hence a+b = -1

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