Q2 of 44 Page 67

Find the quadratic polynomial in each case, with the given numbers as the sum and product of its zeroes respectively.

Given: α + β = √2


Let the quadratic polynomial be ax2 + bx + c …(1)


Where, a≠0


And zeroes of the polynomial are α and β .


Now we know that,




And,



If a = 3



⇒ b = -3√2 …(2)


⇒c = 1 …(3)


From (2) and (3),


a = 3, b = -3 √2 and c = 1


Hence, the polynomial is 3x2 – 3√2x + 1


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