Question

If α and β are zeroes of the polynomial 2x2
- 5x + 7 .Find a polynomial whose zeroes are 2α+β and
2β+3

Answer 1

roots should be 2a + b and 2b+ a

hope u understand, if not msg me

Answer 2

Appropriate Question :-

• If α ,β are the zeroes polynomial p(x)= 2x² -5x +7 , find a quadratic polynomial whose zeroes are 2α + 3β , 3α + 2β

Required Answer :-

• The required polynomial is x² - 5x + 14.

• We have been given that α and β are the zeros of the quadratic polynomial 2x² - 5x + 7.

Find relationship between Zeros :-

• Sum of Zeros = -b/a

• α + β = -(-5)/2

• α + β = 5/2

Product of Zeros = c/a

• αβ = 7/2

• Here, We have to find a Polynomial whose zeros are 2α and 2β.

• Sum of Zeros = 2α + 2β

• Sum of Zeros = 2 ( α + β )

• Sum of Zeros = 2 * 5/2

• Sum of Zeros (α + β) = 5

• → Product of Zeros = 2α * 2β

• → Product of Zeros = 4ab

• → Product of Zeros = 4*7/2

• → Product of Zeros(αβ)= 14

Find a polynomial with the given zeros :-

• f(x) = k[x² - ( α + β)x + αβ]

• f(x) = x² - (5)x + 14

• f(x) = x² - 5x + 14

Therefore, required polynomial is x² - 5x + 14.

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