Q. 3 B4.6( 5 Votes )

# Find the zeroes of the quadratic polynomial 4 x^{2} – 4x – 3 and verify the relationship between the zeroes and the coefficients of the polynomial.

Answer :

Let f(x) = 4 x^{2} – 4x – 3

By splitting the middle term, we get

f(x) = 4 x^{2} – 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 polynomial4x^{2} – 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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