. If α and β are the roots of 2x^2+7x-9=0 then find the equation whose roots are
α/β ,β/α

Step-by-step explanation:

Given Equation is

=>

Comparing it with , we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β =

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

Now, Finding the equation whose roots are:

α/β ,β/α

Sum of Roots =

Sum of Roots =

Sum of Roots =

Sum of roots =

Sum of roots =

Sum of Roots =

Sum of roots =

Sum of roots = S =

Product of Roots =

Product of Roots = P = 1

The Quadratic Equation is:

=>

=>

=>

=>

This is the required quadratic equation.

α/β= -2/9      β/α=-4.5

Step-by-step explanation:

So we have quadratic equation  2x^2+7x-9=0

Lets fin the roots  using the equation's  discriminant:

D=b^2-4*a*c

a=2 (coef at x^2)   b=7(coef at x)  c=-9

D= 49+4*2*9=121

sqrt(D)=11

So x1= (-b+sqrt(D))/(2*a)

x1=(-7+11)/4=1   so   α=1

x2=(-7-11)/4=-4.5    so  β=-4.5

=>α/β= -2/9       => β/α=-4.5

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step-by-step explanation: