Question

If a and B are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a
a-1 B-1
polynomial whose roots are (i) a +2,B+2 (ii)
a +1' B + 1​

Answer 1

Step-by-step explanation:

Given, x = a cos theta and y = b sin theta. Substituting for x and y ,

b²x² + a²y² - a²b² = b²a² cos² theta + a²b² sin² theta - a²b²

= a²b² (cos² theta + sin² theta) - a²b²

= a²b² . 1 - a²b² (Using the trigonometric identity cos² theta + sin² theta = 1)

= a²b² - a²b² = 0 (Proved)

Work 2:

x = a cos theta , y = b sin theta . Substituting for x,

b²x² + a²y² - a²b² = b²a² cos² theta - a²b² + a²y²

= b²a²(cos² theta-1) + a²y²

= b²a²(-sin² theta) + a²y² = -a²(b²sin² theta) + a²y² Substitute y for b sin theta.

=-a²y² + a²y²

= 0 (Proved)