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

Sum

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

8x2 + 2x – 3 = 0

#### 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