Question

If one solution of the equation 3x 2 -8x+2k+1 is seven times the other. Find the solutions and the value of k ?

Answer 1

Solution is attached here

Answer 2

Solution:

Given Quadratic equation

3x²-8x+2k+1 = 0

Compare this with ax²+bx+c =0

we get

a = 3 , b = -8 , c = 2k+1

According to the problem given,

One solution of the equation is seven times of the other.

Let m, 7m are two solutions of the equation.

i ) Sum of the roots = -b/a

=> m+7m = -(-8)/3

=> 8m = 8/3

=> m = 8/(8×3)

=> m = 1/3

=> m² = 1/9 ---(1)

ii) Product of the roots= c/a

=> m × 7m = (2k+1)/3

=> 7m² = (2k+1)/3

=> 7×(1/9) = (2k+1)/3

=> (7/9) × (3/1) = 2k+1

=> 7/3 = 2k+1

=> 7/3 - 1 = 2k

=> (7-3)/3 = 2k

=> 4/3 = 2k

=> 4/(3×2) = k

=> 2/3 = k

Therefore,

k = 2/3

And

Two roots are ,

m = 1/3

7m = 7×(1/3) = 7/3

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