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Find whether the following equation have real roots. If real roots exist, find them 5x2 – 2x – 10 = 0 - Mathematics

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Sum

Find whether the following equation have real roots. If real roots exist, find them

5x2 – 2x – 10 = 0

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Solution

Given equation is 5x2 – 2x – 10 = 0

On company with `ax^2 + bx + c` = 0, we get

a = 5, b = – 2 and c = – 10

∴ Discriminant, D = `b^2 - 4ac`

= `(-2)^2 - 4(5)(-10)`

= 4 + 200

= 204 > 0

Therefore, the equation `5x^2 - 2x - 10` = 0 has two distinct real roots.

Roots, `x = (-b +- sqrt(D))/(2a)`

= `(-(-2) +- sqrt(204))/(2 xx 5)`

= `(2 +- 2sqrt(51))/10`

= `(1 +- sqrt(51))/5`

= `(1 + sqrt(51))/5, (1 - sqrt(51))/5`

Concept: Nature of Roots
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.4 | Q 1.(iii) | Page 42
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