Question

if a and b are zeros of the polynomial x to the power2 -2x-15 then the polynomial whose zeros are 2a and 2b


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Answer 1

Solution :

Let p(x) = x² - 2x -15

On comparing with ax² + bx +C, we get

a =1,b = -2 and c = -15. ......... (1/2)

Given, a and b are the zeroes of p(x).

Sum of zeroes, (a + b) = -b/a

a + b = -2/1

a + b = 2. .........(i)

and product of zeroes, (a - b) = c/a

ab = -15/1

ab = -15. ........(ii)

We have to form a polynomial whose zeroes are 2a and 2b

Sum of zeroes = 2a +2b = 2(a +b)

= 2 x 2= 4 [using Eq. (i)]

and product of zeroes = 2a.2b

= 4ab = 4 x (-15) = -60 [using Eq. (ii)]

Required polynomial

= x² - (Sum of zeroes) x + (Product of zeroes)

= x² - 4x + (-60)

= x² - 4x-60