Home
Class 12
MATHS
If the equation (b^2 + c^2) x^2 -2 (a+b)...

If the equation `(b^2 + c^2) x^2 -2 (a+b) cx + (c^2 + a^2) = 0` has equal roots, then

A

a, b, c are in G.P.

B

`c^2 = ab`

C

a, b, c, are in G.P.

D

`c = sqrt(ab)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS|2 Videos

  • THEORY OF EQUATIONS

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS( CHOOSE THE ADD MAN OUT : )|3 Videos

  • THEORY OF EQUATIONS

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS( Fill in the blanks : )|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

For a , b , c non-zero, real distinct, the equation, (a^(2)+b^(2))x^(2)-2b(a+c)x+b^(2)+c^(2)=0 has non-zero real roots. One of these roots is also the root of the equation :

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

If the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

Prove that the equation x^(2)(a^(2)b^(2))+2x(ac+bd)+(c^(2)+d^(2))=0 has no real root if adnebc .

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then

If the equations x^(2) - ax + b = 0 and x^(2) - ex + f = 0 have one root in common and if the second equation has equal roots, then prove that ae = 2 (b + f).

If the roots of the equation (c^(2)-ab)x^(3)-2(a^(2)-bc)x+b^(2)-ac=0 are real and equal prove that either a=0 (or) a^(3)+b^(3)+c^(3)=3"abc" .

If the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, then a. c(a-b+c)>0 b. c(a+b+c)>0 c. c(4a-2b+c)>0 d. none of these