If alpha and beta are the zeros of the quadratic polynomial of the quadratic . . . .

Question : If α and β are the zeros of the quadratic polynomial x²-2x+b, find b if 3α+2β=20.

Doubt by Aditi

Solution : 

x²-2x+b

Here 

A = 1

B = -2

C = b

Sum of zeros of quadratic polynomial

α+β = -b/a

α+β = -(-2)/1

α+β = 2 — (1)

Also
3α+2β=20 (Given)
3α+2β=20 — (2)

Solving equation (1) and (2) by elimination method 

[α+β = 2]×2

3α+2β=20

2α+2β = 4

3α+2β = 20

-    -        -

----------------
-α + 0 = -16
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-α = -16

α = 16

putting in equation (1)

16+β = 2

β = 2-16

β = -14

Also
Product of zeros of quadratic polynomial 

αβ = C/A
αβ = C/A

αβ = b/1

αβ = b 

16(-14) = b
-224 = b

b=-224

Hence, the required value of b is -224.