Q. 9

# If α and β are the zeros of the quadratic polynomial , find the value of .

Given : α and β are the zeros of the quadratic polynomial
To find : the value of .
Solution : and β are the roots of the given eq.
Sum of root:

Product of the roots:

Now,

Use (a + b)2 = a2 + b2 + 2ab and (a - b)2 = a2 + b2 - 2ab to find the value of β-α.
(β+α)222+2βα
add and subtract 2βα on right hand side of the above equation.
(β+α)222+2βα+2βα-2βα
(β+α)2=(β-α)2+4βα

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