Question

If one zero of polynomial 3x2-8x+2k+1 in seven times other find the zero and the value of the k

Answer 1

1) Let f(x) = 3x2+ 8x + (2k + 1) and α and β be its zeroes
Here a = 3, b = 8 and c = 2k + 1
Given,
α = 7β -(i)
Sum of roots, α + β = -b/a
7β + β = -8/3 [Using (i)]
8β = -8/3
β = -1/3
Putting β = -1/3 in (i), we have
α = 7*-1/3 = -7/3
So, the zeroes are α = -7/3 and β = -1/3
Now,
Product of roots = -1/3*-7/3
c/a = 7/9
(2k + 1)/3 = 7/9
2k + 1 = 7/3
2k = 4/3
k = 2/3
So, value of k = 2/3






3x²-8x+2k+1 a=3, b=-8 ,c=2k+1

suppose the zeroes of the equation are α and β . by the given condition α=7β
as we know , α+β=-b/a
7β+β=-(-8)/3
8β=8/3
β=8/3×1/8=1/3
αβ=c/a
7β×β=2k+1/3
7×1/3×1/3=2k+1/3
7/9=2k+1/3
21/9=2k+1
21/9-1=2k
12/9=2k
4/3=2k
4/6=k
2/3=k