Question

please answer this quedtion​

Answer 1

option : 1) is correct

Given,

$\alpha \: and \beta \: are \: the \: roots \: of \: \\ \: a {x}^{2} + bx + c = 0$

we know that

$\alpha + \beta = \frac{ - b}{a} \\ or \\ \alpha \beta = \frac{c}{a}$

to find the equation whose roots is

$\frac{ \alpha }{ \beta } and \frac{ \beta }{ \alpha }$

so , find the sum of zeroes

and product of zeroes

and put the value in the.

p(x)= x^2 - (sum of zeroes )x +(product of zeroes)

soln refers to the attachment

Answer 2

$\huge{\boxed{\mathtt{\red{ANSWER}}}}$

Let roots are x and y .

sum of roots = -b/a = x+y

product of roots = c/a = xy

we know that, (x+y)² -2xy = x²+y²

putting values we get,

(b²/a²) - 2c/a = x²+y²

(b²-2ca)/a² = x²+y² ----------------------(eqn(1))

Now. roots of new eqn are x/y , y/x

sum of roots = x/y + y/x = (x²+y²/xy)

product of roots = x/y * y/x = 1

putting value of both now we get ,

sum = [(b²-2ca)/a²]/[c/a] = (b²-2ca)/ac

so, required eqn,

x²-sum of rootsx + product of roots = 0

x²-(b²-2ca)/acx + 1 = 0

acx²-(b²-2ca)x + ac = 0 = option A = Answer

$<marquee>Mark as Brainlist$

$<marquee>Mark as Brainlist$$<marquee>Thanks$