Question

two zeros of cubic polynomial ax³+3x²-bx-6 are -1 and -2. find the third zeros and values of a and b​

Answer 1

Given

A polynomial ax³+3x²-bx-6

And their zeroes is -6 and -1

To find

value of a,b and third zeroes

Solution

Let the third zeroes of the polynomial be $\gamma$

putting the value of zeroes X=(-1,-2) in polynomial

First X= -1

f(X}=ax³+3x²-bx-6 =0

f(-1)=-a+3+b-6

=>a+b=3______(1)

second X = -2

F(X)=ax³+3x²-bx-6=0

f(-6)=-8a+12+2b-6

=>-8a+2b=-6

=>4a-b=3

From equation (1) and (2)

a+b=3

4a-b=3

___________

5a=6

a=6/5

b=9/5

Now we know

$\alpha.\beta\gamma=\frac{-d}{a}$

2$\gamma=5$

$\therefore\gamma=\frac{2}{5}$