Question

if the sum of zeroes of the polynomial x^2-(k-3)x+(5k-3) is equal to one fourth of the product of the zeroes find the value of k

Answer 1

For the polynomial x²-(k-3)x+(5k-3)

Sum of the roots = -b/a = (k-3)

Product of the roots = c/a = (5k-3)

As per the question, 
Sum of zeroes = 1/4( product of zeroes)

k-3 = 1/4(5k-3)

4k - 12 = 5k - 3

k = -9

Answer 2

Concept:

The sum of zeros of a quadratic expression is equal to the negative value of the ratio of coefficient of variable with power 1 and coefficient of variable with power 2.

The Product of zeros of a quadratic expression is equal to the value of the ratio of constant term and coefficient of variable with power 2.

For example if the quadratic expression is $ax^2+bx+c$ and the zeros of this equation are m, n then,

m + n = -b/a

mn = c/a

Given:

Given that, the sum of zeroes of the polynomial $x^2-(k-3)x+(5k-3)$ is equal to one fourth of the product of the zeroes

Find:

The value of k.

Solution:

Here the given quadratic polynomial is $x^2-(k-3)x+(5k-3)$

On comparing we get, a = 1, b = -(k-3) and c = 5k-3

Sum of the zeros = -b/a = (k-3)/1 = k-3

Product of zeros = c/a = (5k-3)/1 = 5k-3

According to the condition, the mathematical equation is,

k-3 = 1/4 (5k-3)

4k-12 = 5k-3, multiplying 4 to both sides

5k-4k = 3-12

k = -9

Hence the value of k is given by -9.

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