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find the zeroes of the quadratic polynomial x^2 – 2x – 8 and verify a relationship between zeroes and its coefficients - Mathematics

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find the zeroes of the quadratic polynomial x2 – 2x – 8 and verify a relationship between zeroes and its coefficients

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

x2 – 2x – 8

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Solution 1

f(x) = 𝑥2 − 2𝑥 − 8

𝑓(𝑥) = 𝑥2 − 2𝑥 − 8

= 𝑥2 − 4𝑥 + 2𝑥 − 8

= 𝑥(𝑥 − 4) + 2(𝑥 − 4)

= (𝑥 + 2)(𝑥 − 4)

Zeroes of the polynomials are -2 and 4

Sum of the zeroes `="-coefficient of x"/"coefficient of x"`

`-2+4=(-(-2))/1`

2 = 2

Product of the zeroes `="constant term"/("coefficient of "x^2)`

`-2xx4=(-8)/1`

`-8 = -8`

Solution 2

x2 - 2x- 8 = x2 - 4x + 2x - 8

= x(x-4) + 2(x - 4)

= (x - 4)(x + 2)

Therefore the zeroes of the polynomial x2 - 2x - 8 are {4, 2}

Relationship between the zeroes and the coefficients of the polynomial

Sum of the zeroes = - `(`

Also sum of the zeroes of the polynomial = 4 - 2 = 2

Product of the zeroes = `(`

Also product of the zeroes  = 4 x -2 = -8

Hence verified

Concept: Relationship Between Zeroes and Coefficients of a Polynomial
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Exercise 2.1 | Q 1.1 | Page 33
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