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Find whether the following equation have real roots. If real roots exist, find them 8x2 + 2x – 3 = 0 - Mathematics

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Sum

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

8x2 + 2x – 3 = 0

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Solution

Given equation is 8x2 + 2x – 3 = 0

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

a = 8, b = 2 and c = – 3

∴ Discriminant, D = `b^2 - 4ac`

= `(2)^2 - 4(8)(-3)`

= 4 + 96

= 100 > 0

Therefore, the equation `8x^2 + 2x - 3` = 0 has two distinct real roots because we know that

If the equation `8x^2 + 2x - 3` = 0 has discriminant greater than zero then it has two distinct real roots.

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

= `(-2 +- sqrt(100))/16`

= `(-2 +- 10)/16`

= `(-2 + 10)/16, (-1 - 10)/16`

= `8/16, -12/16`

= `1/2, - 3/4`

Concept: Nature of Roots
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APPEARS IN

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