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
Answers
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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