Q. 3 B5.0( 3 Votes )
Find the zeroes of the quadratic polynomial 4 x2 – 4x – 3 and verify the relationship between the zeroes and the coefficients of the polynomial.
Answer :
Let f(x) = 4 x2 – 4x – 3
By splitting the middle term, we get
f(x) = 4 x2 – 6x + 2x – 3
= 2x(2x – 3) + 1(2x – 3)
= (2x + 1) (2x – 3)
On putting f(x) = 0, we get
(2x + 1) (2x – 3) = 0
⇒ 2x + 1 = 0 or 2x – 3 = 0
or 
Thus, the zeroes of the given polynomial
4x2 – 4x – 3 are 
and 
Verification
Sum of zeroes 
or
Product of zeroes 
or
So, the relationship between the zeroes and the coefficients is verified.
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