Find the nature of the roots of the following quadratic equations.…

Question 7 of 11intermediate🔧 ApplyNumerical2 marks

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:

(i)

$2x^2 - 3x + 5 = 0$

Answer

No real roots exist.

(ii)

$3x^2 - 4\sqrt{3}x + 4 = 0$

Answer

Two equal real roots exist: x = 2 $\sqrt{3}$ /3

(iii)

$2x^2 - 6x + 3 = 0$

Answer

Two distinct real roots exist: x = (3 + $\sqrt{3}$ )/2 and x = (3 - $\sqrt{3}$ )/2

Explanation

This question tests the concept of discriminant and nature of roots from the chapter on Quadratic Equations. The discriminant (b² - 4ac) determines the nature of roots: positive means two distinct real roots, zero means two equal real roots, and negative means no real roots.

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