# Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials: 4x2 – 3x – 1 - Mathematics

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

4x2 – 3x – 1

#### Solution

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 = 3/4

Product of the zeroes = constant term ÷ coefficient of x2

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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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 2 Polynomials
Exercise 2.3 | Q 1.(i) | Page 12
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