Question

Find the zeros of the polynomial 4x2 – 3x– 1 by factorization method and verify the

relations between the zeros and the coefficients of the polynomial​

Answer 1

Answer:

Let f(x)=4x2−3x−1

Splitting the middle term, we get

=4x2−4x+1x−1

=4x(x−1)+1(x−1)

=(x−1)(4x+1)

For f(x)=0, we have

4x2−3x−1=0

or (x−1)(4x+1)=0

Either x−1=0⇒x=1

or 4x+1=0

⇒4x=−1

⇒x=4−1

∴ The zeroes of f(x) are 1 and 4−1.

Verification:

α=1,β=4−1

a=4,b=−3 and c=−1

∴α+β=a−b

⇒1−41=4−(−3)

⇒43=