Question

If α and βare zeros of quadratic polynomial f(x) = x² -x -2. find another quadratic polynomial whose zeros are α/β and β/α.............Please help as soon as possible........... It's very urgent....... ​

Answer 1

Answer:

x²-3x+2=0

=x²-x-2x+2=0

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

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

or ,

x=2 given zeroes of quadratic polynomial 1/2alpha+beta

1/2beta+alpha substitute=1/2(1)+2

1/2(2)+1=1/4

1/5formula is x²-(alpha+beta)x+alpha*beta =0

therefore x²-(1/4+1/5)x+1/4*1/5=0

20x^2 - 9x +1 =0

Answer 2

Quadratic Equation -

=> f ( x ) = x² - x - 2 .

Let us assume that the roots of this equation are α and β

Sum of roots of a Quadratic equation -

=> ( - b / a )

=> ( --1 / 1 )

=> 1

So ,

α + β = 1 .......... ,{1}

Sum of roots of a Quadratic equation -

=> ( c / a )

=> ( -2 / 1 )

=> -2

So ,

α β = -2 ..,......... {2}

Now , roots of the new equation &

=> α/β and β/α

Sum of roots -

=> ( α/β + β/α )

=> ( α² + β² ) / ( αβ )

=>[ ( α + β )² - 2αβ ] / [ αβ ]

=> ( 5 / -2 )

=> -(5/2)

Product Of Roots -

α/β × β/α

=> 1

New Quadratic Equation -

=> x² - ( Sum of roots ) x + ( Product of roots )

=> x² + (5/2) x + 1

This is the required equation .

This is the answer .

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