Determining the nature of roots of Quadratic equation:
Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.4 Q1 Download this solution
1. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them.
(i)
(ii)
(iii)
Solution (i)
Comparing this equation with general equation
, we get
and
.
Discriminant is less than 0 which means equation has no real roots.
Solution (ii)
Comparing this equation with general equation
, we get
and c=4.
Discriminant =
Discriminant is equal to zero which means equations has equal real roots.
Applying quadratic formula
to find roots we get,
Because, equation has two equal roots, it means
.
is also equal to
. Therefore
Solution (iii)
Comparing equation with general equation
, we get
, and
.
Discriminant =
Value of discriminant is greater than zero. Therefore, equation has distinct and real roots.
Applying quadratic formula
to find roots we get,
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