1
Arjuna JEE 2.0 (2023)
Quadratic Equation
1.
2.
3.
4.
5.
6.
7.
If α and β are the roots of the equation,


7x2 – 3x – 2 = 0, then the value of
is
+
2
1− 
1 − 2
equal to
(1) 3/8
(2) 1/24
(3) 27/16
(4) 27/32
If the roots of the equation x2 – 8x + (a2 – 6a) = 0 are
real, then
(1) –2 < a < 8
(2) 2 < a < 8
(3) –2  a  8
(4) 2  a  8
The number of integral values of m for which the
equation (1 + m2) x2 – 2(1 + 3m)x + (1 + 8m) = 0 has
no real roots is :
(1) 2
(2) Infinitely many
(3) 1
(4) 3
8.
Find p and q such that px2 + 5x + 2 = 0 and 3x2 + 10x
+ q = 0 have both roots in common.
9.
If the quadratic equations x2 + ax + b = 0 and x2 + bx
+ a = 0 (a  0) have a common root, then the
numerical value of (a + b) is
(1) 0
(2) 1
(3) −1
(4) 2
10.
Find the value of m for which the quadratic equations
x2 – 11x + m = 0 and x2 – 14x + 2m = 0 may have
common root.
11.
If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0,
a, b, c  R, have a common root, then a : b : c is:
(1) 1 : 2 : 3
(2) 3 : 2 : 1
(3) 1 : 3 : 2
(4) 3 : 1 : 2
12.
If both the root of k (6x2 + 3) + rx + 2x2 – 1 = 0 and
6k (2x2 + 1) + px + 4x2 – 2 = 0 are common, then
2r – p is equal to
(1) –1
(2) 0
(3) 1
(4) 2
13.
If the equation x2 + px + q = 0 and
x2 + qx + p = 0, have a common root,
then p + q + 1 =
(1) 0
(2) 1
(3) 2
(4) –1
14.
If the roots of the equation 2x2 – 3x + 5 = 0 are
reciprocals of the roots of the equation ax2 + bx + 2
= 0, then
(1) a = 2 and b = 3
(2) a = 2 and b = –3
(3) a = 5 and b = –3
(4) a = 5 and b = 3
15.
If the quadratic equation 3x2 + ax + 1 = 0 and
2x2 + bx + 1 = 0, have a common real root, then the
value of the expression 5ab – 2a2 – 3b2 is
(1) 0
(2) 1
(3) –1
(4) none of these
If the equation (k2 – 3k + 2)x2 + (k2 – 5k + 4)x
+ (k2 – 6k + 5) = 0 is an identity then the value of k is
(1) 1
(2) 2
(3) 3
(4) 4
If a + b + c = 0 and a, b, c are rational, then the
roots of the equation (b + c – a)x2 + (c + a – b)x
+ (a + b – c) = 0 are
(1) Rational
(2) Irrational
(3) Imaginary
(4) Equal
The quadratic equation whose roots are reciprocal of
the equation ax2 + bx + c = 0 is
(1) cx2 + bx + a = 0
(2) bx2 + cx + a = 0
(3) cx2 + ax + b = 0
(4) bx2 + ax + c = 0
2
2
If the equations ax + bx + c = 0 and x + x + 1 = 0
has one common root then a : b : c is equal to
(1) 1 : 1 : 1
(2) 1 : 2 : 3
(3) 2 : 3 : 1
(4) 3 : 2 : 1
DPP-03
2
Note: Kindly find the Video Solution of DPPs Questions in the Quiz Section.
Answer Key
1.
(3)
9.
(3)
2.
(3)
10. (24 or 0)
3.
(2)
11. (1)
4.
(1)
12. (2)
5.
(1)
13. (1)
6.
(1)
14. (3)
7.
(1)
15. (2)
8.
(p=
3
,q = 4 )
2
For more questions, kindly visit the library section: Link for app: https://links.physicswallah.live/vyJw
For more questions, kindly visit the library section: Link for web: https://physicswallah.live/tabs/tabs/library-tab
PW Mobile APP: https://physicswala.page.link/?type=contact-us&data=open
For PW Website: https://www.physicswallah.live/contact-us