Question

If a and b are zeroes of the polynomial x²-x – 4, form a quadratic polynomial
whose zeroes are 1/a and 1/b.

Answer 1

The required answer is in attachment.

Answer 2

Hi !

p(x) =  x²-x – 4
a and b are zeros of p(x)

a + b = 1
ab = -4

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polynomial with zeros 1/a and 1/b

sum of zeros = 1/a + 1/b = a+b/ab
                                        = 1/-4 = -1/4

product of zeros = 1/a*1/b = 1/ab = -1/4

a quadratic polynomial is given by :-

x² - (sum  of zeros)x + (product  of zeros)

hence, the polynomial whose zeros are 1/a and 1/b is :-

x² + 1/4x -1/4 

or

4x² + x - 1