Home
Class 12
MATHS
If the sum of the roots of the quadratic...

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.

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    SURA PUBLICATION|Exercise 3 MARKS|5 Videos

  • PROBABILITY DISTRIBUTIONS

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS - 5 MARKS|4 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY - II

    SURA PUBLICATION|Exercise ( 5 marks )|5 Videos

Similar Questions

Explore conceptually related problems

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 is equal to the sum of the squares of their reciprocals, then (a)/(c ), (b)/(a)" and "(c )/(b) are in

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.

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

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

The sum of square of roots of the equation 2x^4+x^2+x+2=0 is :

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.

Find the sum of the squares of the roots of ax^4+bx^3+cx^2+dx+e = 0 , a ne 0 .

Find the value of k for which the sum of the squares of the reciprocals of the roots of x^(2)+kx+9=0is(2)

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