Question

if the sum of squares of the zeroes of the polynomials 6x^2+x+k is 25/36. find the value of k?

Answer 1

Let the zeroes be a, b.
Given a²+b²=25/36

We also have, 6x²+x+k = 0
Sum of roots ( a+ b) = -1/6
Product of roots (a*b) = k/6 .

a²+b² = (a+b)²-2ab

25/36 =( -1/6)²-2(k/6)

25/36-1/36 = -2k/6

24/36 =-2 k/6

4/6 = -2k/6

2k = -4

k = -2

Therefore, K = -2 .

Answer 2

Answer:

Step-by-step explanation:

Let the zeroes be a, b.

Given a²+b²=25/36

We also have, 6x²+x+k = 0

Sum of roots ( a+ b) = -1/6

Product of roots (a*b) = k/6 .

a²+b² = (a+b)²-2ab

25/36 =( -1/6)²-2(k/6)

25/36-1/36 = -2k/6

24/36 =-2 k/6

4/6 = -2k/6

2k = -4

k = -2

Therefore, K = -2 .

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