Question

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
please give me the correct answer or I will report it
correct answer will be marked as the brainiest

Answer 1

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

Answer 2

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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