Question

If a,ß are the roots of the equation
x? +7x+12=0, then equation whose roots
are (a+beta)^2
&(a - beta )^2 is

(a) x + 50x +49 = 0
(b) x2 - 50x +49 = 0
(c) x² – 50x - 49=0
(d) x? +12x + 7 = 0​

Answer 1

Answer:

x^2 +7x+12 gives a+b = -7 and ab=12

We calculate a-b first

(a-b)^2 = (a+b)^2 -4ab =(-7)^2-4×12 =1

Now the equation whose roots are (a+b)^2 and (a-b)^2 will be

x^2 -{(a+b)^2 +(a-b)^2}x + (a+b)^2.(a-b)^2

=x^2-{49+1}x +49×1

=x^2-50x +49....