Question

find the quadratic equation whose roots exceed the roots of the quadratic equation xsqiate​

Answer 1

Let f(x) = x² - 2x + 3.

Suppose a and b are the roots, so f(a) = f(b) = 0.

We want a polynomial g(x) that has roots a+2 and b+2.

So we want

g(a+2) = g(b+2) = 0.          ... (*)

Take g(x) = f(x-2).

Then g(a+2) = f( (a+2) - 2 ) = f(a) = 0

and g(b+2) = f( (b+2) - 2 ) = f(b) = 0.

So this is the quadratic that satisfies (*).

The quadratic that we want is then

g(x) = f(x-2) = (x-2)² - 2(x-2) + 3

= x² - 4x + 4 - 2x + 4 + 3

= x² - 6x + 11