Question

If two zeroes of the polynomial f(x)=x^3-5x^2-2x+24 are root 3 and -root3 then find its third zero

Answer 1

Product of zeroes of a cubic polynomial is -d/a of cubic polynomial ax^3 + bx^2 + cx + d 
So we know product of two zeroes therefore by putting value of product of two zeroes and taking third as a variable we get third zero as -2 
Therefore -2 satisfies the equation and x+2 will be a factor of the equuation 

By diving the above equation by x+2 we will get a quadratic rquation 
I.e. x^2 -7x + 12 
Now by splitting the middle term you can find the other two zeroes 
i.e. x^2 - 4x -3x + 12 
X(x - 4) -3(x - 4) 
Therefore (x-3)(x-4)= x^2 - 4x -3x + 12 
Therefore the other two zeroes are 3 and 4 

The zetoes for the cubic equation are -2, 3 , 4 
To verify you can put these values in the equation and find answer = 0