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## Question 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (vi)3x² – x – 4

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

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