**1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.**

(vi)3x² – x – 4

(vi) 3x² – x – 4

Factorize the equation

3x² – x – 4

Compare the equation with ax² + bx + c = 0

We get

a = 3 ,b=-1 c= -4

to factorize the value we have to find two value which

sum is equal to b =-1

product is a*c = 3*-4 = -12

3 and -4 are such number which

Sum is 3 – 4 = - 1

Product is 3 *- 4 = - 12

So we can write middle term -x = 3x – 4x

We get

3x² + 3x - 4x - 4 = 0

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

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

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

Solve for first zero

x = - 1

solve for second zero

3x-4 = 0

3x = 4

x = 4/3

Sum of zeros -b/a = -(-1/3) = 1/3

Product of zero c/a = -4/3 = 4/3