Question

Q3. (a) If a and B are the roots of equation x² – 3x + 2 = 0, form the equation whose roots are (a + b)2 and
(a - b)?​

Answer 1

Step-by-step explanation:

x² -3x +2=0

x²-2x-x+2= 0

x(x-2)-1(x-2)=0

(x-2)(x-1)=0

Therefore x= 1,2 are the roots of the equation.

let a= 2 and b = 1

Now,

(a+b)² and a-b are roots of the equation that is to be found,so first we need to find the values of the roots by putting the values a and b.

Therefore,

(a+b)²= (2+1)²=3²=9

a-b= 2-1 = 1

The roots of the unknown equation are 9 and 1.

The equation can be calculated as,

x²-[(a+b)²+(a-b)]x +[(a+b)²(a-b)]

as we now know the values of roots,

The equation is x²-(9+1)x+(9×1)

= x²-10x+9