# Find whether the following equation have real roots. If real roots exist, find them x2+55x-70 = 0 - Mathematics

Sum

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

x^2 + 5sqrt(5)x - 70 = 0

#### Solution

Given equation is x^2 + 5sqrt(5)x - 70 = 0

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

a = 1, b = 5sqrt(5) and c = - 70

∴ Discriminant, D = b^2 - 4ac

= (5sqrt(5))^2 - 4(1)(-70)

= 125 + 280

= 405 > 0

Therefore, the equation x^2 + 5sqrt(5)x - 70 = 0 has two distinct real roots.

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

= (-5sqrt(5) +- sqrt(405))/(2(1))

= (-5sqrt(5) +- 9sqrt(5))/2

= (-5sqrt(5) + 9 sqrt(5))/2, (-5sqrt(5) - 9sqrt(5))/2

= (4sqrt(5))/2, - (14 sqrt(5))/2

= 2sqrt(5), -7sqrt(5)

Concept: Nature of Roots of a Quadratic Equation
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10