Question

66) The equation ax^2+bx+ a=0and
x^3-2x^2+2x-1=0have two
roots comman
then
(a+b)​

Answer 1

Step-by-step explanation:

ax2+bx+a=0 has two roots and both these roots are common to two of the roots ofx3−2x2+2x−1

Since it is a quadratic equation so either both the roots are real or both the roots are imaginary since if one root is imaginary then the other root must also be imaginary (imaginary roots occur in pairs, one being the conjugate of the other)

x3−x2−x2+x+x−1=0⟹(x−1)(x2−x+1)=0

Roots of this equation has one real root and two imaginary roots.

This means that if x=1 satisfies our equation ax2+bx+a=0then the other root must be imaginary which isnt possible as either both root can be real or both will be imaginary. Hence the possible roots are the roots of the equation x2−x+1=0

Comparing this equation to ax2+bx+a=0we get-

a1=b−1=a1=t(say)

Hence, a=tandb=−t

Therefore,a+b=0