Question

find the zeroes of the polynomial 4x2-3x-1 and verify the relationship between the zeroes and the coefficients of the polynomial

Answer 1

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Answer 2

Answer:

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