Question

if -1 and -2 are the zeros of ax3+3x2-bx-6,find the third zero and values of a and b

Answer 1

Hey!

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p (x)= ax^3 + 3x^2 - bx - 6

If - 1 and -2 are the zeroes of p(x)

x = -1

Putting the values,

p ( -1) = a (-1)^3 + 3 (-1)^2 - b (-1) - 6 = 0

-a + 3 + b - 6 = 0

-a + b = 3 ------------- (i)

Now,

x = -2

p (-2) = a (-2)^3 + 3 (-2)^2 - b (-2) - 6 = 0

-8a + 12 + 2b - 6 = 0

-8a + 2b = -6 ------------- (ii)

Now,

Multiplying (i) with 2

-2a + 2b = 6
-8a + 2b = -6

Now , subtracting (ii) from (i)

We will get,

6 a = 12

a = 2

Now, putting value of a in (i)

- a + b = 3

- 2 + b = 3

b = 3+2

b = 5

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Third zero =>

Zeroes are -1 and -2

Factors are -

(x + 1) ( x + 2)

= x^2 + 3x + 2

g (x) = x^2 + 3x + 2

Now divide p (x) by g (x)
After that , quotient will be 2x - 3

2x - 3 = 0

x = 3/2

Thus, third zero is 3/2

Answer 2

hope this helps you ☺☺