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Revision Quiz | Quadratic Equations and Polynomial
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Question 1
Two distinct polynomials f(x) and g(x) are defined as follows:
f(x)=x2 + ax+ 2 ; g(x)=x2 +2x+a
If the equations f(x)=0 and g(x)=0 have a common root
then the sum of the roots of the equation f(x)+ g(x)=0 is
f(x)=x2 + ax+ 2 ; g(x)=x2 +2x+a
If the equations f(x)=0 and g(x)=0 have a common root
then the sum of the roots of the equation f(x)+ g(x)=0 is
Question 2
Let p(x) = x2 – 5x + a and q(x) = x2 – 3x + b, where a and b are positive integers. Suppose HCF(p(x), q(x)) = x – 1 and k(x) = LCM(p(x),q(x)). If the coefficient of the highest degree term of k(x) is 1, the sum of the roots of (x ‒ 1) + k(x) is
Question 3
The number of possible value of 'α' for which the expression y = 
has atleast one common linear factor in numerator and denominator, is -
has atleast one common linear factor in numerator and denominator, is - Question 4
For 
, 
and 
are the roots. Find the value of 
.
, and are the roots. Find the value of . Question 5
If α,β,γ are the roots of the equation 
, then the equation whose roots are (α-β)(α-γ),(β-γ)(β-α),(γ-α)(γ-β) is ____.
, then the equation whose roots are (α-β)(α-γ),(β-γ)(β-α),(γ-α)(γ-β) is ____. Question 6
If 7/2 and 1 are the roots of the equation
then the third root is:
then the third root is:Question 7
Let 
be real numbers between -5 and 5 such that
Then the product
is
be real numbers between -5 and 5 such that Then the product
isQuestion 8
If 
and
are the roots of the equation x2+ px + q = 0 where 
,
, p and q are real, then the roots of the equation (p2–4q)(p2x2+4px)– 16q = 0
and are the roots of the equation x2+ px + q = 0 where ,, p and q are real, then the roots of the equation (p2–4q)(p2x2+4px)– 16q = 0 Question 9
If a, b, c are three distinct positive real numbers then the number of real roots of ax2 + 2b |x| – c = 0 is
Question 10
The range of the values of 
for all real value of x is-
for all real value of x is- Question 11
If c > 0 and b > c then x2 + bx – c = 0 will have-
Question 12
If x2 + 2ax + a < 0 ∀ x∈[1,2] ,then find values a
Question 13
All the value of m for which both the roots of the equation x2 – 2mx + m2 – 1 = 0 are greater than -2 but less than 4, lie in the interval
Question 14
Form the cubic equation whose roots are greater by unity than the roots of 
.
. Question 15
Let r be a real number and 
be such that the polynomial divides 
the polynomial 
Then (n, r) can be
be such that the polynomial divides the polynomial Then (n, r) can be- 364 attempts
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Dec 18JEE & BITSAT
