Question

The sum of zeroes and product of zeroes of polynomial 4x²−3x−1 is ______ respectively * 2 points 3/4 and −1/4 −1/4 and 3/4 1/4 and 3/4 None of the above​

Answer 1

Step-by-step explanation:

4x² – 3x – 1

Splitting the middle term, we get,

4x²-4x+1x-1

Taking the common factors out, we get,

4x(x-1) +1(x-1)

On grouping, we get,

(4x+1)(x-1)

So, the zeroes are,

4x+1= 0⇒ 4x=-1 ⇒x= (-1/4)

(x-1) = 0 ⇒ x=1

Therefore, zeroes are (-1/4) and 1.

Verification:

Sum of the zeroes = – (coefficient of x) ÷ coefficient of x²

α + β = – b/a

1 – 1/4 = – (- 3)/4 = ¾

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

1(- 1/4) = – ¼

– 1/4 = – 1/4