Question

if alpha and beta are the zeros of polynomial 2x2+x-6 ,then form a quadratic equation whose zeros are 2alpha and 2 beta

Answer 1

2x²+x-6
⇒2x²+4x-3x-6
⇒2x(x+2)-3(x+2)
⇒(2x-3)(x+2)
⇒x=3/2 and x=-2
let alpha = 3/2 and beta = -2
so 2 alpha and 2 beta is ⇒ 2×3/2=3= 2 alpha and 2 beta = -4
so now 2 alpha+ 2 beta = 3+(-4)=-1
and 2 alpha × 2 beta = 3×(-4)= -12
so are quadratic equation will be x² -( sum of zeroes)x + (product of zeroes)
⇒x²-(-1)x+(-12)
⇒x²+x-12

Answer 2

Step-by-step explanation:

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