If α and β are the zeroes of the quadratic polynomial p(x) = x2 – 3x + 7 find a quadratic polynomial whose zeroes are 1/∝ and 1/β<

2 thoughts on “If α and β are the zeroes of the quadratic polynomial p(x) = x2 – 3x + 7 find a quadratic polynomial whose zeroes are 1/∝ and 1/β<”

1. Answer:

   Given polynomial is x²-3x+7

   It’s zeroes are the solutions to the quadratic equation

   x²- 3x +7 = 0

   Now from the theory of equations, we can say,

   α + β = 3

   αβ = 7

   We have to find a quadratic equation whose roots are 1/α and 1/β.

   From the theory of equations,

   Sum of Roots S = (1/α + 1/β) = (α+β)/αβ = 3/7

   Product of Roots P = 1/αβ = 1/7

   The required quadratic equation is x² – Sx + P = 0

   Or x² – (3/7)x + (1/7) = 0

   Or 7x² – 3x + 1 = 0

   This is the answer.

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2. Step-by-step explanation:

   Let,

   x²-3x-2=0

   x²-2x-x-2=0

   -x(-x-2)+1(-x-2)=0

   (-x-2)(-x+1)=0

   -x-2=0 (or) -x+1=0

   -x=2. (or) -x= -1

   x= -2 (or) x=1

   Sum of roots= -2+1= -1

   product of roots= -2×1= -2

   Quadratic equation:-

   X²- (sum of roots) X + product of roots=0

   X²-(-1)X+(-2)=0

   X²+X-2=0

   Thank you

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