Question

if α and β are the zeroes of the poly. 4x²+4x+1 then form a quadratic poly. whose zeroes are 2α and 2β

Answer 1

Hey mate!!

f(x) = 4x^2 + 4x +1

suppose roots = a & b

then, a+ b = -b/a = -1 .......(1)eqn

also, ab = c/a = 1/4 ...........(2)eqn

let, another polynomial be g(x)

g(x) = ax^2 + bx +c

zeroes = 2a and 2b

2a + 2b = -b/a

2(a +b) = -b/a

2x(-1) = -b/a ..... from eqn (1)

-2 = -b/a

2= b/a .........(3) eqn

also, 2a × 2b = c/a

4(ab) = c/a

4 × 1/4 =c/a...... from eqn 2

1 = c/a.....(4)eqn

from 3 and 4

a=1 , b=2, c =1

equation g(x) = x^2 + 2x +1

hope it helps!

#JaiHind