Question

If a and b are the zeros of the polynomial x2-4x+3 then form a quadratic equation whoes zeros are 3a and 3b

Answer 1

Hey there,

x=3a
then a=x/3

(x/3)²-4(x/3)+3
=x²/9-4x/3+3
Multiplying by 9, we get-

x²-12x+27

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Answer 2

Hi !

p(x) = x² - 4x + 3

sum of zeroes = a + b = -(-4) = 4
product of zeros = ab = 3

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A quadratic polynomial is of the form :-

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

sum of zeros = 3a + 3b = 3(a+b)
                                      = 3*4 = 12

product = 3a*3b = 9b
                          = 9*3
                          = 27

Hence, the polynomial is :-

x² - 12x + 27