Question

if alpha and beta are the zeros of x square - 6 X + K what is the value of k if 3 alpha + 2 B tech 20.
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Answer 1

Let alpha = p and beta = q.

Given Polynomial:

x² - 6x + k

Let a = 1 ; b = - 6 ; c = k

We know that,

sum of the zeroes = - b/a

→ p + q = - (- 6)/1

→ p + q = 6 -- equation (1)

Product of the zeroes = c/a

→ pq = k -- equation (2)

And also given that,

3p + 2q = 20 -- equation (3)

Multiplying equation (1) by 2 and subtracting equation (1) from (3) we get,

→ 3p + 2q - 2(p + q) = 20 - 2(6)

→ 3p + 2q - 2p - 2q = 20 - 12

→ p = 8

Substitute "p = 8" in equation (1)

→ p + q = 6

→ 8 + q = 6

→ q = 6 - 8

→ q = - 2

Putting the values of p & q in equation (2) we get,

→ (8)( - 2) = k

→ k = - 16

Hence, the value of k is - 16.

Answer 2

SOLUTION ::

α. . β. x², θ ➙

The given equation is x² - 6x + k = 0 - - - - - (1)

Since α, β are the zeros of the equation

So

α + β = Sum of the zeroes = - (-6)/1 = 6 - - - - - - (2)

αβ = Product of the Zeros = k/1 = k - - - - (3)

Again by the given condition

3α + 2β = 20 - - - - - - - (4)

From Equation (2) & Equation (4) we get

3α + 2( 6 - α) = 20

➙ 3α - 2α = 20 - 12

➙ α = 8

So

β = 6 - 8 = - 2

So From Equation (3)

k = 8 × (-2) = - 16