Problem of relations between the coefficients of a quadratic equation.how

Troszokd95

Troszokd95

Answered question

2022-04-22

Problem of relations between the coefficients of a quadratic equation.how to proceed?
If the roots of ax2+bx+c=0 are of the form λλ1 and λ+1λ, then the value (a+b+c)2 in terms of a, b, c is?
Options
(a)b24ac
(b)b22ac
(c)2b2ac
(d)4b22ac
(e)b24abc

Answer & Explanation

mandamosppy

mandamosppy

Beginner2022-04-23Added 21 answers

ca=λλ1×λ+1λ =λ+1λ1λ=c+acax1=λλ1 =c+a2ax2=λ+1λ =2cc+aba=x1+x2 =(c+a)2+4ac2a(c+a)2b(c+a)=(c+a)2+4ac0=(c+a)2+2b(c+a)+4acb24ac=(c+a)2+2b(c+a)+b2(a+b+c)2=b24ac

botassaiby

botassaiby

Beginner2022-04-24Added 16 answers

Define f(x)=ax2+bx+c then
f(x)=ax2+bx+c=a(xλλ1)(xλ+1λ)
Hence (a+b+c)2=(f(1))2=a2(1-λλ-1)2(1-λ+1λ)2¯a21(λ-1)21λ2=a2(λλ-1-λ+1λ)2¯a2(r-s)2=a2((r+s)2-4rs)¯a2(-b/a)2-4a2(c/a)=b2-4ac
where r=λλ1 and s=λ+1λ

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