Question

If α, β are zeros of x² - 6x + k. What is the value of k if 3α + 2β = 20:
1. 8
2. -8
3. -2
4. -16

Answer 1

Correct Answer - Option 4 : -16

Formula used: 

For a quadratic equation ax² + bx + c = 0

Sum of roots = -b/a

Product of roots = c/a

Calculation:

Given that, α, β are zeros of x2 - 6x + k

Then, sum of roots

⇒ α + β = 6  

⇒ 2α + 2β = 12       -----(1)

And product of root

αβ = k                   -----(2)

Also, according to question,

3α + 2β = 20       -----(3)

Substracting equation (1) from equation (3), we will get

α = 8

From equation (1)

2 × 8 + 2β = 12

⇒ β = -2

Therefore, 

k = αβ = 8 × (-2) = -16 

Hence, option 4 is correct.