Question

EXAMPLE 10 ) If a and B are the zeros of the quadratic polynomial f(x) = x - x - 2, find a
polynomin whose zeros 2a+1 & 2b +1 CLASS X R.D SHARMA PAGE 2.29​

Answer 1

Answer:

if a and b are zeroes of the polynomial x²-x-2

then a+b = -b/a

a+b= -(-1)/1

a+b = 1

also,

a*b= c/a

a*b=-2/1

a*b = -2

so finding the polynomial whose zeroes are 2a+1 and 2b+1

formula for the same is:

x²-(sum of zeroes)x+(product of zeroes)

x²-(2a+1+2b+1)x+(2a+1)(2b+1)

x²-(2(a+b)+2)x+(2a(2b+1)+1(2b+1))

x²-(2+2)x+(4ab+2a+2b+1)

x²-4x+(-8+2(a+b)+1)

x²-4x+(-8+2+1)

x²-4x+(-5)

so, the polynomial whose zeroes are 2a+1 and 2b+1 is

x²-4x-5

hope it helps you