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

Sum

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

–2x2 + 3x + 2 = 0

Solution

Given equation is –2x2 + 3x + 2 = 0

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

a = –2, b = 3 and c = 2

∴ Discriminant, D = b^2 - 4ac

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

= 9 + 16

= 25 > 0

Therefore, the equation -2x^2 + 3x + 2 = 0 has two distinct real roots because we know that if the equation ax^2 + bx + c = 0 has its discriminant greater than zero

Then it has two distinct real roots.

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

= (-3 +- sqrt(25))/(2(-2))

= (-3 +- 5)/(-4)

= (-3 + 5)/(-4), (-3 - 5)/(-4)

= 2/(-4), (-8)/(-4)

= - 1/2, 2

Concept: Nature of Roots
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NCERT Mathematics Exemplar Class 10