The abscissa and ordinate of the points A and B are the roots of the equation $x^{2} + 2 a x + b = 0$ and $x^{2} + 2 c x + d = 0$ respectively, then equation of circle with AB as diameter is

Q. (i) lf

α, β

are the roots of

a x^{2} + b x + c = 0

. lf

K

is a real number

[K \neq 0, 1]

then the equation whose roots are

K α, K β

a x^{2} +

Kbx

+ K^{2} c = 0

.
(ii) 8,2 are roots of

x^{2} + a x + β = 0

and 3, 3 are the roots of

x^{2} + α x + b = 0

then the roots of

x^{2} + a x + b = 0

are 9, 1.
Which of the above statement is correct

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I: If x+2 is factor of x2+2ax+b and x2+2cx+d, then b−da−c=4II: The equation whose roots are the squares of the roots of x2+4x+5=0 is x2−6x+25=0 Which of the above statement(s) is/are true?

The correct option is B Both I and IIx+2 is a factor ⇒x=−2 is a root of the given equations .4−4a+b=0;4−4c+d=0b−4a=d−4c⇒b−da−c=4Equation whose root are squares of x2+4x+5 is(√x)2+4√x+5=0x+5=−4√x(x+5)2=(4√x)2x2+25x+10x=16xx2−6x+25=0

I: If $x + 2$ is factor of $x^{2} + 2 a x + b$ and $x^{2} + 2 c x + d$ , then $\frac{b - d}{a - c} = 4$
II: The equation whose roots are the squares of the roots of $x^{2} + 4 x + 5 = 0$ is $x^{2} - 6 x + 25 = 0$
Which of the above statement(s) is/are true?