Home
Class 12
MATHS
The equations ax^(2) + bx+ c =0, x^(3) -...

The equations `ax^(2) + bx+ c =0, x^(3) -2x^(2) +2x -1 =0` have tow roots common, then find the value of a+b.

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \( a + b \) given that the equations \( ax^2 + bx + c = 0 \) and \( x^3 - 2x^2 + 2x - 1 = 0 \) have two common roots. ### Step-by-Step Solution: 1. **Identify the roots of the cubic equation**: The cubic equation is given as: \[ x^3 - 2x^2 + 2x - 1 = 0 ...
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

The equation ax^(2)+bx+c=0 and x^(3)-4x^(2)+8x-8=0 have two roots in common. Then 2b + c is equal to _______.

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

If the equations ax^2 + bx + c = 0 and x^3 + x - 2 = 0 have two common roots then show that 2a = 2b = c .

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 two equations x^(2) + ax + bc = 0 and x^(2) + bx + ca =0 have a common root, the find the condition and the quadratic with other roots of the equations.

If the quadratic equations 3x^2 + ax + 1 = 0 and 2x^2 + bx + 1 = 0 have a common root then the value of 5ab-2a^2-3b^2 , where a b in R , is equal to

If the quadratic equation 3x^(2) + ax+1=0 and 2x^(2) + bx+1=0 have a common root , then the value of the expression 5ab-2a^(2)-3b^(2) is

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 the equations x^2+ax+b=0 and x^2+bx+a=0 have one common root. Then find the numerical value of a+b.

If the equations ax^2 + bx + c = 0 and x^2 + x + 1= 0 has one common root then a : b : c is equal to