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## Question 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (iii) 6x² – 3 – 7x

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(iii) 6x² – 3 – 7x

(iii) 6x² – 3 – 7x
Factorize the equation
6x² – 7x – 3
Compare the equation with ax²  + bx  + c  = 0
We get
a = 6 ,b=-7 c= -3
To factorize the value we have to find two value which
sum is equal to              b                     =-7
product is                    a x c  = 6 x -3    = -18
2 and -9 are such number which
sum is                          2 – 9                = - 7
product is                    2 x - 9               = - 18
So we can write middle term       -7x      = 2x – 9x
We get

6x² + 2x - 9x - 3 = 0
2x(3x + 1) -3(3x + 1) = 0
(3x + 1) (2x - 3) = 0
3x + 1 = 0 , 2x - 3 = 0
Solve for first zero
3x        = - 1
x          = -1/3
Solve for second zero
2x-3     = 0
2x        = 3
X          = 3/2

Plug the values of a , b and c we get
Sum  of zeros             -b/a     = -(-7/6)           = 7/6
Product of zero           c/a      =  -3/6             = -1/2

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Question 1. Find the zeroes of the following quadratic polynomials and verify the relation