Question

find he zeroes of the polynomial -x²+4x-3=0

Answer 1

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 polynomial4x2 – 4x – 3 areand

Verification

Sum of zeroesor



Product of zeroesor



So, the relationship between the zeroes and the coefficients is verified.