Question

if the equation x^2-15x+k=0 and their Ratio is 2:3 find the value of k​

Answer 1

Step-by-step explanation:

This is a quadratic equation and I've attached the solution

Answer 2

Given:

x²-15x+k = 0

Roots ratio = 2:3

To Find:

The value of k.

Solution:

We are required to find the value of k.

The given equation is x²-15x+k = 0

Let α and β be the roots of the equation.

Compare  x²-15x+k = 0 with  ax²+bx+c = 0

a = 1, b = -15, c = k

Sum of roots = α+β = -b/a

α+β = 15  ---------(1)

Product of roots = αβ = c/a

αβ = k     ---------(2)

It is given that the ratio of roots is 2:3.

α:β = 2:3

α/β = 2/3

α = 2β/3

Substitute the value of α in equation(1) we get

2β/3 + β = 15

5β/3 = 15

5β = 45

β = 45/5

β = 9

Now substitute the value of β in equation(1) we get α

α + 9 = 15

α = 15-9

α = 6

Now substitute the value of α and β in equation(2) we get the value of k

6×9 = k

k = 54

Therefore, The value of K is 54.

#SPJ2