Home
Class 12
MATHS
Find a relation between a,b,c so that tw...

Find a relation between a,b,c so that two quadratic equations ` ax^(2) + bx + c =0 and 1003x^(2) + 1505x + 2007 =0` have a common root.

Text Solution

AI Generated Solution

To find a relation between \( a, b, c \) such that the quadratic equations \( ax^2 + bx + c = 0 \) and \( 1003x^2 + 1505x + 2007 = 0 \) have a common root, we can follow these steps: ### Step 1: Let the common root be \( \alpha \). Assume that \( \alpha \) is a common root of both equations. Therefore, we have: \[ a\alpha^2 + b\alpha + c = 0 \quad \text{(1)} \] \[ ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|60 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

If a,b,c, in R and equations ax^(2) + bx + c =0 and x^(2) + 2x + 9 = 0 have a common root then

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

If a + b + c = 0 then the quadratic equation 3ax^(2) + 2bx + c = 0 has

If the quadratic equation ax^(2) + 2cx + b = 0 and ax^(2) + 2x + c = 0 ( b != c ) have a common root then a + 4b + 4c is equal to

If d,e,f are G.P. and the two quadratic equations ax^(2)+2bx+c=0anddx^(2)+2ex+f=0 have a common root, then

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

The quadratic equation ax^(2)+bx+c=0 has real roots if:

If a,b,c in R and equations ax^2 + bx + c = 0 and x^2 + 2x + 9 = 0 have a common root, show that a:b:c=1 : 2 : 9.

If x^(2) + ax + b = 0, x^(2) + bx + a = 0 ( a != 0 ) have a common root, then a + b =

If the equation x^(2 )+ 2x + 3 = 0 and ax^(2) +bx+c=0, a, b, c in R , have a common root, then a : b:c is