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Byju's Answer
Standard X
Mathematics
Formation of Quadratic Equation from Roots
Of the follow...
Question
Of the following quadratic equations, which is the one whose roots are
2
and
−
15
?
A
x
2
−
2
x
+
15
=
0
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B
x
2
+
15
x
−
2
=
0
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C
x
2
+
13
x
−
30
=
0
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D
x
2
−
30
=
0
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Solution
The correct option is
C
x
2
+
13
x
−
30
=
0
Quadratic equation with roots 2 and -15 will be
(
x
−
2
)
(
x
+
15
)
=
0
x
2
+
15
x
−
2
x
−
30
=
0
x
2
+
13
x
−
30
=
0
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0
Similar questions
Q.
Roots of quadratic equations
x
2
−
13
x
−
30
=
0
is
Q.
Find the discriminant of the following quadratic equations and discuss the nature of the roots .
1.
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x
+
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=
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2.
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=
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=
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Q.
The quadratic equation whose roots are A.M and H.M of the roots of the equation
x
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Q.
Choose the correct answers for the following questions.
(1) Which one is the quadratic equation ?
(A)
5
x
-
3
=
x
2
(B) x(x + 5) = 2
(C) n – 1 = 2n
(D)
1
x
2
x
+
2
=
x
(2) Out of the following equations which one is not a quadratic equation ?
(A) x
2
+ 4x = 11 + x
2
(B) x
2
= 4x
(C) 5x
2
= 90
(D) 2x – x
2
= x
2
+ 5
(3) The roots of x
2
+ kx + k = 0 are real and equal, find k.
(A) 0
(B) 4
(C) 0 or 4
(D) 2
(4) For
2
x
2
-
5
x
+
2
=
0
find the value of the discriminant.
(A) –5
(B) 17
(C)
2
(D)
2
2
-
5
(5) Which of the following quadratic equations has roots 3,5 ?
(A) x
2
– 15x + 8 = 0
(B) x
2
– 8x + 15 = 0
(C) x
2
+ 3x + 5 = 0
(D) x
2
+ 8x – 15 = 0
(6) Out of the following equations, find the equation having the sum of its roots –5.
(A) 3x
2
– 15x + 3 = 0
(B) x
2
– 5x + 3 = 0
(C) x
2
+ 3x – 5 = 0
(D) 3x
2
+ 15x + 3 = 0
(7)
5
m
2
-
5
m
+
5
=
0
which of the following statement is true for this given equation ?
(A) Real and uneual roots
(B) Real and equal roots
(C) Roots are not real
(D) Three roots.
(8) One of the roots of equation x
2
+ mx – 5 = 0 is 2; find m.
(A) –2
(B)
-
1
2
(C)
1
2
(D) 2
Q.
Let
A
=
{
x
∈
R
:
x
2
−
|
x
|
−
2
=
0
}
and
B
=
{
α
+
β
,
α
β
}
where
α
,
β
are real roots of the quadratic equation
x
2
+
|
x
|
−
2
=
0
.
If
(
a
,
b
)
∈
A
×
B
,
then the quadratic equation whose roots are
a
,
b
is
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