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Formation of a Quadratic Equation From It's Roots

If alpha and ...

Question

If alpha and beta are zeros of polynomial 6x²- 7x - 3, then form a quadratic polynomial whose zeros are 2 alpha and 2 Beta.

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Solution

6x²-7x-3=0
6x²-9x+2x-3=0
3x(2x-3)+1(2x-3)=0
(3x+1)(2x-3) = 0
X = 3/2, -1/3

Alpha= 3/2
Beta = -1/3

2alpha = 3
2 Beta = -2/3

Eq. (X+2alpha )(x+2Beta)
(X+3)(x-2/3)=0
X²-2x/3+3x-2=0
X²+7x/3-2= 0

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Formation of a Quadratic Equation From It's Roots

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