Login/Sign Up
Home » Find the nature of roots of the following quadratic equations:(i) (ii)
Find the nature of roots of the following quadratic equations:
(i) 5 x^{2}-4 x+1=0
(ii) 5 x(x-2)+6=0
CBSE | Class 10 | Exercise 10D | Maths | Quadratic Equations | RS Aggarwal
Find the nature of roots of the following quadratic equations:
(i) 5 x^{2}-4 x+1=0
(ii) 5 x(x-2)+6=0

(i) The given equation is 5 x^{2}-4 x+1=0
This is of the form a x^{2}+b x+c=0, where a=5, b=-4 and c=1.
\therefore Discriminant,
D=b^{2}-4 a c=(-4)^{2}-4 \times 5 \times 1=16-20=-4<0
Hence, the given equation has no real roots.

(ii) The given equation is
\begin{array}{l} 5 x(x-2)+6=0 \\ \Rightarrow 5 x^{2}-10 x+6=0 \end{array}
This is of the form a x^{2}+b x+c=0, where a=5, b=-10 and c=6.
\therefore Discriminant,
D=b^{2}-4 a c=(-10)^{2}-4 \times 5 \times 6=100-120=-20<0
Hence, the given equation has no real roots.

i

More Material