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Byju's Answer
Standard XII
Mathematics
Nature of Roots
Check whether...
Question
Check whether the following equation will have two distinct real or imaginary or two real equal roots.
x
2
−
3
x
+
5
=
0
.
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Solution
Given the quadratic equation is
x
2
−
3
x
+
5
=
0
.
Now discriminant of this equation will be
b
2
−
4
a
c
=
(
−
3
)
2
−
4
×
5
×
1
=
9
−
20
=
−
11
.
As the discriminant
<
0
then the quadratic equation will have imaginary roots.
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0
Similar questions
Q.
(1)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(i)
x
2
−
3
x
+
4
=
0
(2)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(ii)
2
x
2
+
x
−
1
=
0
(3)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(iii)
2
x
2
−
6
x
+
9
2
=
0
(4)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(iv)
3
x
2
−
4
x
+
1
=
0
(5)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(v)
(
x
+
4
)
2
−
8
x
=
0
(6)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(vi)
(
x
−
√
2
)
2
−
2
(
x
+
1
)
=
0
(7)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(vii)
√
2
x
2
−
3
√
2
x
+
1
√
2
=
0
(8)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(viii)
x
(
1
−
x
)
−
2
=
0
(9)
State whether the following quadratic equation have two distinct real roots. Justify your answer
(ix)
(
x
−
1
)
(
x
+
2
)
+
2
=
0
(10)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x)
(
x
+
1
)
(
x
−
2
)
+
x
=
0
Q.
Check whether
2
x
2
−
3
x
+
5
=
0
has real roots or no.
Q.
Check whether the roots of the following quadratic equations are real or not?
3
x
2
−
4
√
3
x
+
4
=
0
.
Q.
The nature of roots of
x
2
−
3
x
+
2
=
0
will be:
Q.
The equation
x
2
+
x
−
5
=
0
has two distinct real roots.
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