 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,i5i
 a+ib,aib
 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
 has one root 3
 Show that 1 is a root of the equation x^2+(2abc)x+(c+a2b)=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
 and

 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 be in the ratio of 3:4, prove that

 If are the roots of the equation , prove that
 If roots of the equation be in the ratio of p:q, prove that
 If are the roots of the equation , prove that
 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