Question

Find the value of ‘k’ so that the zeros of the quadratic polynomial 3x2 – kx + 14 are in
the ratio 7:6.

Answer 1

Answer:

Step-by-step explanation:

0

Answer 2

Answer:

k = 13

Step-by-step explanation:

Sol:

 If α,β are the roots of the equation ax2 + bx + c = 0.

 α + β = -b / a and αβ = c / a.

 If α,β are in the ratio 7:6

then

α / β = 7 / 6.

 ∴ α  = 7β / 6.

 If α,β are the roots of the equation 3x2 - kx + 14 = 0. 

α + β = k / 3 ----------(1) 

And αβ = 14 / 3

⇒ 7β^2 / 6 = 14 / 3 .           [ α  = 7β / 6] 

⇒ β^2  = 4 .

 ∴ β = 2 and α  = 7 / 3. 

Substitute α , β are roots in equation (1) 

⇒ (7 / 3) + 2 = k / 3

 ⇒ 13 / 3 = k / 3

 ∴ k = 13.

Hope it helps.

:)