Please solve question 35 Q 35 If the two equations x2-cx+d=0 x2-ax+b=0 have one common root and - Maths - Complex Numbers and Quadratic Equations

Question

Please solve question 35
Q 35 If the two equations x 2 - c x + d = 0 & x 2 - a x + b = 0
have one common root and the second has equal roots, then 2 (b + d)
=
[1] 0
[2] a + c
[3] ac
[4] - ac

Lovina Kansal · Accepted Answer

Dear student
Let α,β be the roots of x2-cx+d=0    
(1)and α,α be the roots of the equation x2-ax+b=0    
(2)So, α be satisfy both the equations
i e
, α2-cα+d=0=α2-aα+b⇒α2-cα+d=α2-aα+b⇒-cα+d=-aα+b⇒αa-c=b-d⇒α=b-da-c    
(A)From eq(2),Sum of roots=2α=-Coeff
 of xCoeff of x2=a    
(B)Product of the roots=α2=Constant termCoeff
 of x2=b     
(C)From (B), we have2α=a⇒2b-da-c=a   [using A]⇒2b-d=a(a-c)⇒2(b-d)=a2-ac     
(D)From (C), we haveα2=b⇒a22=b     [using B]⇒a2=4bPut the value of a2 in (D), we have2(b-d)=4b-ac⇒2b-2d=4b-ac⇒2b+2d=ac⇒2(b+d)=ac
Regards

Please solve question 35 Q.35. If the two equations x 2 - c x + d = 0 & x 2 - a x + b = 0 have one common root and the second has equal roots, then 2 (b + d) = [1] 0 [2] a + c [3] ac [4] - ac

Please solve question 35
Q.35. If the two equations $x^{2} - c x + d = 0$ & $x^{2} - a x + b = 0$ have one common root and the second has equal roots, then 2 (b + d) =
[1] 0
[2] a + c
[3] ac
[4] - ac