Question

find the zeroes of the 3X²-x-4are verify the relationship between the zeroes and the coefficients​

Answer 1

Step-by-step explanation:

3x^2-x-4=0

3x^2-x(4-3)-4

3x^2-4x+3x-4=0

x(3x-4)+1(3x-4)=0

x+1=0 , 3x-4=0

x=-1,x=4/3

Addition of zeroes =-b/a

-b/a = -1+4/3

-(-1)/3=-1/1+4/3

1/3=-3+4/3

1/3=1/3

Product of zeroes = c/a

-1/1*4/3=-4/3

-4/3=-4/3

Answer 2

Answer:

4/3 and -1 are the zeroes of the polynomial 3x^2-x-4

Step-by-step explanation:

3x^2-x-4

=3x^2-(4x-3x)-4

=3x^2-(-3x+4x)-4

=3x^2+3x-4x-4

=3x(x+1)-4(x+1)

=(3x-4)(x+1)

So, either values of 3x-4 or x+1 can be zero.

so now, 3x-4

=x= 4/3 can be a zero

and. x+1

=x=-1 can be another one

Now, alpha + beta = -b/a

= 4/3 + -1 = 1/3

=1/3 = 1/3

and. alpha × beta = c/a

= 4/3 × -1 = -4/3

= -4/3 = -4/3

Hence, verified

I hope that it will be helpful to you !