- Determine the nature of roots of each of the following equations
- For what values of p will the equation
?
- if the equation
has equal roots, find k.
- For what value of a will the equation
have equal roots?
- If the roots of the equation
are equal, then show that
- Show that the roots of the equation
will be equal, if either
or
- If
are rational and
, show that the roots
are rational.
- Prove that the roots of the equation
are real for all values of k.
- Show that the roots of the equation
are imaginary.
- If the roots of the quadratic equation
are real and unequal, prove that the roots of the equation
are imaginary
Category: Grade 11 Mathematics
Quadratic Equation [BCB Ex6.2]
- From the equation whose roots are
- 3,-2
- -5,4
- -3+5i,-i-5i
- a+ib,a-ib
- 3,-2
-
- Find a quadratic equation whose roots are twice the roots of
- Find a quadratic equation whose roots are reciprocals of the roots of
- Find a quadratic equation whose roots are greater by h than the roots of
- Find a quadratic equation whose roots are the squares of the roots of
- Find a quadratic equation whose roots are twice the roots of
- Find a quadratic equation with rational coefficients one of whose roots is
- Find the value of k so that the equation
has one root 3
has roots whose sum is equal to 6
has roots equal but opposite in sign
has roots numerically equal but opposite in sign
has one root equal to zero
has the reciprocal roots
has roots whose difference is
- Show that -1 is a root of the equation
x^2+(2a-b-c)x+(c+a-2b)=0\). Find the other root.
- Find the value of m for which the equation
will have (a) reciprocal roots (b) one root zero.
- If the roots of the equation
differ by 1, prove that
- If
are the roots of the equation
, find the equation whose roots are
- If
are the roots of the equation
, find the equation whose roots are
and
and
and
- the reciprocal of the roots of given equation
-
- If the roots of the equation
be in the ratio of 3:4, prove that
- If one root of the equation
be four times the other root, show that
- For what values of m, the equation
may have its root in the ratio 2:3
- If the roots of the equation
-
- If
are the roots of the equation
, prove that
- If roots of the equation
be in the ratio of p:q, prove that
- If
- If one root of the equation
be square of the other root, prove that
Quadratic Equation[BCB Ex6.3]
- Show that each pair of following equations has a common root
- Find the value of p so that each pair of the equations may have one root common
- If the quadratic equations
and
have common roots show that it must be either
or
- If the quadratic equations
and
have common roots show that it must be either
or
- If the quadratic equations
and
have common roots show that it must be either
or
- Prove that if the equations
and
have a common root, their other root will satisfy