Question

If no. Of apples and mangoes are zeroes of polynomial3x²=8x-2k+1 and the no. Of apples is seven times tha no. Of mangoesthen find the zeroes and valie of k.

Answer 1

Solution:

Given polynomial is 3x^2 = 8x - 2k + 1
Let no. of zeroes of mangoes be X and no. of zeroes of apples be 7X.

or, 3x^2 = 8x
or, 3x = 8
or, x = 8/3

or, 3x^2 = -2k + 1
or, x^2 = (-2k + 1)/3

Now, sum of zeroes:

or, X + 7X = 8/3
or, 8X = 8/3
or, X = 1/3 = Zeroes (Answer)

Now, product of zeroes:

or, X.7X = (-2k + 1)/3
or, 21X^2 = (-2k + 1)
or, 21(1/3)^2 = (-2k + 1)
or, 21.(1/9) = -2k + 1
or, 7/3 - 1 = -2k
or, (7 - 3)/3 = -2k
or, k = - 4/6
or, k = - 2/3 (Answer)