Question

If the roots of the equation x2
- 10x + k = 0 with variable
'x' are in the ratio 2 : 3, what is the value of 'k' ?

Answer 1

Answer:

f(x) = x^2 - 10x + k = 0

first case when x = 2

f (2) = (2)^2 - 10×2 + k = 0

f(2) = 4 - 20 +k = 0

f(2) = -16 + k = 0

f(2) = k = 16

second case x = 3

f(3) =( 3)^2 - 10 x3 + k = 0

f(3) = 9 - 30 + k = 0

f(3) = -21 + k = 0

f(3) = k = 21

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Answer 2

The value of 'k' = 24.

Given:

• x² - 10x + k = 0
• Ratio of their roots 2:3.

To find:
Value of k

Step by step explanation:

Step 1:
For a quadratic equation,
a² + bx + c = 0 let the roots for the above equation be 's' and 't'.
Now, s + t = -b/a                                                        (1)
         s * t = c/a                                                          (2)

Step 2:
Now, according to question,
s : t = 2 : 3
Let s = 2y and t = 3y

Step 3:
Putting the values of 's' and 't' in (1)
⇒ 2y + 3y = - (-10)/1
⇒ 2y = 10
⇒ y = 10/2
⇒ y = 2

Step 4:
Now, putting the values of 's' and 't' in (2)
⇒ 2y * 3y = k/1
⇒ 6y² = k                                                                (3)

Step 5:
Putting value of y = 2 in (3)
⇒ 6 * 2 * 2 = k
⇒ k = 6 * 4
⇒k = 24

∴ The value of 'k' = 24.

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