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.

4, 1

Given: α + β = 4

αβ = 1


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 = 1



⇒ b = -4 …(2)


⇒c = 1 …(3)


From (2) and (3),


a = 1, b = -4 and c = 1


Hence, the polynomial is x2 - 4x + 1


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