Question

find the zeros of the quadratic equation 3x square -x-4 and verify the relationship between the zeros and the coefficient?

Answer 1

Given that

3x² - x - 4

= 3x² - 4x + 3x -4

=  x (3x  - 4 ) + 1 ( 3x - 4)

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

So zero of the quadratic equation 3x² - x - 4 when 3x² - x - 4 = 0

So

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

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

x = 4/3    or x = -1

So zero of 3x² - x - 4 are 4/3 and -1

Now sum of zeros = 4/3 - 1 = (4 - 3)/3 = 1/3 = - (coeff. of x/coeff. of x² )

And product of zeros = (4/3)×(-1) = -4/3 =  (constant term /coeff. of x² )

Hence Proved.