Question

if alpha and beta are the zeros of quadratic polynomial x^2-6x+α find the value of Alpha if 3α+2β=20
hint...:- answer is 16​

Answer 1

Step-by-step explanation:

Given Equation is x² - 6x + a.

Here a = 1, b = -6, c = a

(i) Sum of zeroes:

α + β = -b/a

α + β = 6

(ii) Product of zeroes:

αβ = c/a

αβ = a

(iii)

Given Equation is 3α + 2β = 20

On solving (i) * 2 & (iii), we get

2α + 2β = 12

3α + 2β = 20

---------------------

α = 8

Substitute α = 8 in (i), we get

α + β = 6

⇒ 8 + β = 6

⇒ β = -2

Substitute β = -2 in (ii), we get

⇒ αβ = a

⇒ a = -16

Hope it helps!

Answer 2

Polynomial   P(x) = x² - 6 x + a

Given  α and  β  are the roots.     To find a , if 3 α + 2 β = 20.  ---(1)

From the quadratic expression:

   α + β = 6       ---(2)

   and   α β = a  --- (3)

Multiply equation (2) by 2 and subtract from (1) to get:

   α = 20 -12 = 8

Substitute this value in(2) to get:    

    β = 6-8 = -2  

Substitute these in (3) to get:    a = α β = -16.