If the sum of the roots of the quadratic...

If the sum of the roots of the quadratic equation `ax^(2)+bx+c=0` is equal to the sum of the squares of their reciprocals, then `(a)/(c ), (b)/(a)" and "(c )/(b)` are in

geometric progression

harmonic progression

arithmetic- geometric progression

arithmetic progression

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMPLEX NUMBERS AND QUADRATIC EQUATIONS
NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos
BINOMIAL THEOREM
NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos
CONIC SECTIONS
NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equl to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.P.

If the sum of the roots of the quadratic equation ax^(2) + bx + c = 0 is equal to the sum of the squares of their reciprocals, then prove that 2a^(2)c = c^(2)b + B^(2)a.

If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 ( abc ne 0) is equal to the sum of the squares of their reciprocals, the sum of the squares of their reciprocals, then a/c , b/a , c/b are in H.P.

Show that the sum of roots of a quadratic equation ax^(2)+bx+c=0 (a ne 0) is (-b)/(a) .

If the sum and product of the roots of the equation ax^(2)-5x+c=0 are both equal to 10 then find the values of a and c.

The condition that one root of the equation ax^(2)+bx+c=0 may be square of the other is

If the roots of the equation ax^(2)-4x+a^(2)=0 are imaginery and the sum of the roots is equal to their product then a is

Show that the product of the roots of a quadratic equation ax^(2)+bx+c=0 (a ne 0) is (c )/(a) .

the quadratic equation 3ax^2 +2bx+c=0 has atleast one root between 0 and 1, if

If the both roots of the equation x^(2)-bx+c=0 be two consecutive integers, then b^(2)-4c equals

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS

If a,b , c are distinct +ve real numbers and a^(2)+b^(2)+c^(2)=1" then...
Text Solution
|
The value of a for which one root of the quadratic equation (a^(2)-5a+...
Text Solution
|
If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 is equ...
Text Solution
|
The number of real solution of the equation x^(2)-3|x|+2=0 is
Text Solution
|
If ((1+i)/(1-i))^(x)=1, then
Text Solution
|
If z and omega are two non-zero complex numbers such that |z omega|=1"...
Text Solution
|
Let z(1)" and "z(2) be two roots of the equation z^(2)+az+b=0, z being...
Text Solution
|
Let two numbers have arithmetic mean 9 and geometric mean 4. Then thes...
Text Solution
|
If (1-p) is a root of quadratic equation x^(2)+px+(1-p)=0 then its roo...
Text Solution
|
If one root of the equation x^(2)+px+12=0 is 4, while the equation x^(...
Text Solution
|
Let z, omega be complex numbers such that bar(z)+ibar(omega)=0" and "a...
Text Solution
|
If z= x-iy" and "z^(1/3)= p+iq, then (((x)/(p)+(y)/(q)))/((p^(2)+q^(2)...
Text Solution
|
If |z^(2)-1|=|z^(2)|+1, then z lies on
Text Solution
|
If z(1)" and "z(2) are two non-zero complex numbers such that |z(1)+z(...
Text Solution
|
If omega=(z)/(z-(1/3)i)" and "|omega|=1, then z lies on
Text Solution
|
If the cube roots of unity are 1, omega, omega^(2) then the roots of t...
Text Solution
|
The value of a for which the sum of the squares of the roots of the eq...
Text Solution
|
If the both roots of the equation x^(2)-bx+c=0 be two consecutive inte...
Text Solution
|
If the both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 ...
Text Solution
|
Find the derivative of x^(n)+ax^(n-1)+a^(2)x^(n-1)+ . . .+a^(n-1)x+a^(...
Text Solution
|