If the two equations x 2- cx + d =0 and x 2- ax + b =0 have one common roots and the second equation has equal roots then 2(b+d)=

Question

If the two equations x 2- cx + d =0 and x 2- ax + b =0 have one common roots 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/cb25a3696bc9c3bfef16ef6b9fe0535b-.png" /> α+β= c , α ⋅ β= d , α2= b , 2 α= a Now, 2(b+d)=2(α2+α β)=2 α(α+β)= ac.

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

0

$a + c$

ac

$- a c$

$α + β = c, α \cdot β = d, α^{2} = b, 2 α = a$
Now, $2 (b + d) = 2 (α^{2} + α β) = 2 α (α + β) =$ ac.

Q. If the two equations x2−cx+d=0 and x2−ax+b=0 have one common roots and the second equation has equal roots then 2(b+d)=

0

a+c

ac

−ac

α+β=c,α⋅β=d,α2=b,2α=a Now, 2(b+d)=2(α2+αβ)=2α(α+β)= ac.

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

$a + c$

$- a c$

$α + β = c, α \cdot β = d, α^{2} = b, 2 α = a$
Now, $2 (b + d) = 2 (α^{2} + α β) = 2 α (α + β) =$ ac.