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Home » Find the nature of roots of the following quadratic equations:(i) (ii)
Find the nature of roots of the following quadratic equations:
(i) 2 x^{2}-8 x+5=0
(ii) 3 x^{2}-2 \sqrt{6} x+2=0
CBSE | Class 10 | Exercise 10D | Maths | Quadratic Equations | RS Aggarwal
Find the nature of roots of the following quadratic equations:
(i) 2 x^{2}-8 x+5=0
(ii) 3 x^{2}-2 \sqrt{6} x+2=0

(i) The given equation is 2 x^{2}-8 x+5=0
This is of the form a x^{2}+b x+c=0, where a=2, b=-8 and c=5.
\therefore Discriminant,
D=b^{2}-4 a c=(-8)^{2}-4 \times 2 \times 5=64-40=24>0
Hence, the given equation has real and unequal roots.

(ii) The given equation is 3 x^{2}-2 \sqrt{6} x+2=0.
This is of the form a x^{2}+b x+c=0, where a=3, b=-2 \sqrt{6} and c=2.
\therefore Discriminant, D=b^{2}-4 a c=(-2 \sqrt{6})^{2}-4 \times 3 \times 2=24-24=0
Hence, the given equation has real and equal roots.

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