Page 5 - Lesson Notes-Relationhip between Zeroes and coefficients Ch-2 (Polynomals)

Example: If α and β are zeroes of a quadratic polynomial of x – 25, then
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form a quadratic polynomial whose zeroes are 1 + α and 1+ β

Sol: Let p (x)=. x – 25
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For finding the zeroes of p(x),put p(x) = 0, we can get x – 25= 0, x = 5 or –5
Let α = 5 and β = –5
Now 1 + α = 1+5 = 6 and 1+ β = 1+(–5)= –4
Sum of zeroes = (1 + α) + (1+ β) = 6+(–4)=2,
product of zeroes = ( 1 + α)( 1+ β) = 6(–4) = –24
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The required quadratic equation is x – (sum of two zeroes)x + product of
zeroes = 0
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i.e.x – 2x –24 = 0.

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