Discuss the nature of the roots of the following quadratic equations : x2−12x+4x2-12x+4x^2 - (1)/(2)x + 4 = 0

Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0

Sum

`x^2 - (1)/(2)x + 4` = 0

Here a = 1, b = `-(1)/(2)`, c = 1
∴ D = b² - 4ac
= `(-1/2) - 4 xx 1 xx 4`

= `(1)/(4) - 16`

= `-(63)/(4)`
∵ D < 0
∴ Roots are not real.

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