Question

If alpha and beta are the twi zeros of the polynomial 21y2-y-2 find a quadratic polynomial whose zeros are 2alpha and 2 beta

Answer 1

Answer:

$21y2-2y-8=0$

Step-by-step explanation:

given:

alpha and beta are the zeros of the polynomial

$21y^2-y-2\:\\a=21,b=-(-1),c=(-2)\\\\\alpha +\beta =\dfrac{-b}{a}\\\\\alpha *\beta =\dfrac{c}{a}\\\\\implies\:\alpha +\beta =\dfrac{-(-1)}{21}\:\implies\:\dfrac{1}{21}\\\\\alpha *\beta=\dfrac{-2}{21} \\\\if\:2\alpha \:and\:2\beta \:are\:zeros\\\implies\:2\alpha +2\beta =2(\alpha +\beta )=2*\dfrac{(1)}{21}=\dfrac{2}{21}\\\\similarly,2\alpha *2\beta =4(\alpha *\beta )=4*\dfrac{-2}{21}=\dfrac{-8}{21}\\\\\implies\: a=21,\:b=-2,\:c=-8\\\\\implies x^2+(\alpha +\beta )x+\alpha *\beta =0\\using\:it\:$

$\implies\:21y^2-2y-8=0$

Answer 2

I don't know the answer