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If Two Zeros X3 + X2 − 5x − 5 Are √ 5 and − √ 5 , Then Its Third Zero is - Mathematics

MCQ

If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is

Options

  •  1

  • −1

  • 2

  • −2

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Solution

Let `alpha = sqrt5` and `beta= -sqrt5` be the given zeros and y  be the third zero of x3 + x2 − 5x − 5 = 0 then

By using `alpha +beta + y = (-text{coefficient of }x^2)/(text{coefficient of } x^3)`

`alpha + beta + y = (+(+1))/1`

`alpha + beta + y = -1`

By substituting `alpha = sqrt5` and `beta= -sqrt5` in `alpha +beta+y = -1`

`cancel(sqrt5) - cancel(sqrt5) + y = -1`

` y = -1`

Hence, the correct choice is`(b)`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Q 22 | Page 63
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