Question

Find the Zeroes and verify
Relationship between the zeroes and
The co-officients.
6x²-7x-3 ​

Answer 1

Step-by-step explanation:

6x²-9x+2x-3

3x(2x-3)+1(2x-3)

(2x-3)(3x+1)

2x-3=0 or 3x+1=0

x=3/2 or x= -1/3

Relationship between the zeroes and coefficients

1. sum of zeroes = alpha+ beta

-b/a = 3/2+(-1/3)

-(-7)/6= 3/2-1/3

7/6= 9-2/6

7/6= 7/6

2. product of zeroes = (alpha)(beta)

c/a = (3/2)(-1/3)

-3/6 = -1/2

-1/2= -1/2

Answer 2

Step-by-step explanation:

• since we know that if the solution of ax^2+bx+c=0 is x1 and x2 then x1+ x2=-b/a
• and products of zeroes(root) =c/a

6x^2-7x-3=0

upon Factorization

(2x-3)(3x+1)=0

then zeroes are x1= 3/2, x2=-1/3

since x1+x2=-b/a

then -b/a=7/6 and by above solution we also get x1+x2=7/6

and also x1*x2=-3/6=3/2*-1/3=-1/2