Question

if alpha and beta are zeroes of the polynomial x2-5x+6,find a Quadratic polynomial whose zeroes are 2 alpha - 1 and 2 beta -1​

Answer 1

Solution

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Since α,β are the zeroes of the polynomial f(x)=x

2

−2x−3

α+β=−

a

b

=−(−2)=2

αβ=

a

c

=−3

sum of the zeroes of the required polynomial

=(2α−1)+(2β−1)=2(α+β)−2

=2×2−2=2

product of the zeroes =(2α−1)(2β−1)

4αβ−2α−2β+1

=4×−3−2(α+β)+1

=−12−2×2+1=−15

sum of zeroes =2=−

a

b

product of zeroes =−15=

a

c

If a=1, then b=−2,c=−15 in ax

2

+bx+c

The required polynomial is x

2

−2x−15