If the two equations x3-c x+d=0 and x3-a x+b=0 have one common root and the second equation has equal roots, then 2(b+d)=

Question

If the two equations x3-c x+d=0 and x3-a x+b=0 have one common root and the second equation has equal roots, then 2(b+d)= (A) 0 (B) a+c (C) ac (D) -ac

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6bb29223ad4ad932d730eb105b35bb98-.png" /> (x-(a/2))2=((a2/4)-b) ⇒ a2 =4 b ..........(i) x =(a/2).............(ii) α2-c α+d=0 α2-a α+b=0 α=((d-b/c-a)) and from (ii) is (a/2) (a/2)=(d-b/c-a)=2 d-2 b=a c-a2 . from (i) .a2=4 b 2(b+d)=a c

Q. If the two equations $x^{3} - c x + d = 0$ and $x^{3} - a x + b = 0$ have one common root and the second equation has equal roots, then $2 (b + d) =$

$0$

$a + c$

$a c$

$- a c$

Q. If the two equations x3−cx+d=0 and x3−ax+b=0 have one common root and the second equation has equal roots, then 2(b+d)=

0

a+c

ac

−ac

(x−2a​)2=(4a2​−b) ⇒a2=4b..........(i) x=2a​.............(ii) α2−cα+d=0 α2−aα+b=0 α=(c−ad−b​) and from (ii) is 2a​ 2a​=c−ad−b​=2d−2b=ac−a2 { from (i) a2=4b} 2(b+d)=ac

Q. If the two equations $x^{3} - c x + d = 0$ and $x^{3} - a x + b = 0$ have one common root and the second equation has equal roots, then $2 (b + d) =$

$0$

$a + c$

$a c$

$- a c$