Question

Find the value of k' such that the quadratic polynomial x2 - (k + 6) x + 2 (2k +1) has sum of the zeros is half of their product

Answer 1

Answer:

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Answer 2

The value of k = 5.

Given:

The quadratic polynomial x^2 - (k + 6) x + 2 (2k +1) has sum of the zeros is half of their product.

To Find:

The value of k.

Solution:

Let us consider the general form of a quadratic equation:

ax^2 + bx + c

Here,

Sum of roots = -b/a

Product of roots = c/a

In the given equation:

x^2 - (k + 6) x + 2 (2k +1)

Sum of roots = k+6

Product of roots = 2(2k+1)

Given that sum = product/2

=> k+6 = 2(2k+1)/2

=> k+6 = 2k+1

=> k = 5

Hence, the value of k is 5.

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