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Sum

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

4x^{2} – 3x – 1

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#### Solution

4x^{2} – 3x – 1

Splitting the middle term, we get,

4x^{2} – 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 x^{2}

α + β = `– b/a`

`1 – 1/4 = – (- 3)/4 = 3/4`

Product of the zeroes = constant term ÷ coefficient of x^{2}

αβ = `c/a`

`1(-1/4) = - 1/4`

`-1/4 = -1/4`

Concept: Relationship Between Zeroes and Coefficients of a Polynomial

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