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. If α and β are the roots of

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

2 Answers

5 votes

Answer:

α/β= -2/9 β/α=-4.5

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

User Peter Petrus
by
8.2k points
3 votes

Answer:


18x^2+85x+18 = 0

Explanation:

Given Equation is

=>
2x^2+7x-9=0

Comparing it with
ax^2+bx+c = 0, we get

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

So,

Sum of roots = α+β =
-(b)/(a)

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 =
(\alpha )/(\beta ) + (\beta )/(\alpha )

Sum of Roots =
(\alpha^2+\beta^2 )/(\alpha \beta )

Sum of Roots =
((\alpha+\beta )^2-2\alpha\beta )/(\alpha\beta )

Sum of roots =
((-7)/(2) )^2-2((-9)/(2) ) / (-9)/(2)

Sum of roots =
(49)/(4) + 9 /(-9)/(2)

Sum of Roots =
(49+36)/(4) / (-9)/(2)

Sum of roots =
(85)/(4) * (2)/(-9)

Sum of roots = S =
-(85)/(18)

Product of Roots =
(\alpha )/(\beta ) (\beta )/(\alpha )

Product of Roots = P = 1

The Quadratic Equation is:

=>
x^2-Sx+P = 0

=>
x^2 - (-(85)/(18) )x+1 = 0

=>
x^2 + (85)/(18)x + 1 = 0

=>
18x^2+85x+18 = 0

This is the required quadratic equation.

User Spangen
by
7.7k points

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