Question

if the quadratic equation X square + bx + c is equals to zero an x square + bx + b is equals to zero is not equals to see have a common root then prove that there are not uncommon roots are the roots of the equation X square + X + BC is equal to zero

Answer 1

First of all, we will find the roots of the 2nd equation i.e. the one which has given co-efficients,1.[math]x^3 - 2x^2 + 2x - 1 = 0[/math]2.[math](x-1) (x^2-x+1) = 0[/math]Now, the thing to observe is that,complex roots always occur in conjugate pairs(1)So, the possible common roots are*.[math]1[/math]*.the two complex roots of[math]x^2-x+1=0[/math]Using (1), we can say the common roots can only bethe roots of[math]x^2-x+1 =0[/math]because 1and a complex root won't exist together asthe equation is quadratic so there are only two rootsand the complex root won't be able to form a conjugatepair.So,Roots of[math]ax^2+bx+c=0 [/math]and[math]x^2-x+1 =0 [/math]are equal.Thus,[math]ax^2+bx+c=k(x^2-x+1)[/math][math] [/math]where k∈ Z & k!=0,Taking k to be 1,(actually it can takenasany integerexceptzero)[math]ax^2+bx+c=(x^2-x+1) [/math]Thus,[math]a= 1 , b=-1[/math]Finally ,[math] a+b=1+(-1)=[/math]0

Answer 2

Step-by-step explanation:

above. is the answer

I think it would help you all

study hard and if it helps you mark me as brainliest