Question

ifa and b are the zeroes of the quadratic polynomial f(x)=3x^2-4x+1, then find a quadratic polynomial whose zeroes are a-1/a+1 and b-1/b+1​

Answer 1

Step-by-step explanation:

zeros of the polynomial f(x)=3x^2-4x+1 are a and b

then-

a+b= -b/a( here b.and a are from the quadratic equation ax^2-bx+c

a + b = -(-4)/3

a + b = 4/3----1

ab = c/a

ab = -1 /3

quadratic polynomial whose zeroes are a-1/a+1 and b-1/b+1

f(x) = x^2 - ( sum of the roots )x + product of the zeros

f(x) = x^2 - ( a +b + 1+1-(1/a+1/b))x + (a-1/a+1)(b-1/b+1)

f(x) = x^2 - (4/3+ 2 - (b+a/ba))x + ab-a/b+a+1/ab-1/a+b-1/b+1)

f(x) = x^2 - (4/3+2-(4/3/-1/3))x + -1/3-a/b-1/a-1/b + 4/3+1/-1/3+1

f(x) x^ 2 - (4/3+2+4)x + 1+1-3+4 -a/b

f(x) = x^2 - 22x/6 + 3-a/b

to find the value of a/b

we need to find the value of a and b

a-b = (a+b)^2-4ab

a-b= (4/3)^2-(4)(-1/3(

a-b = 16/9+4/3

a- b = 16+12/9

a-b = 28/9-----2

add 1 and 2

2a= 40/9

a= 20/9

b=-8/9

a/b = 20/9/-8/9

a/b= -5/2

f(x) = x^2 - 22x/6 + 3-a/b

f(x) = x^ 2 -22x/6 + 3 -(-5/2)

f(x) = x^2 -22x)6 +3+5/2

f(x) = x^2 -22x/6 +11/2

hope this helps u

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