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Home > Algebra calculators > If `alpha` and `beta` are roots of quadratic equation, then find equation whose roots are `alpha^2` and `beta^2` calculator
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Solution
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Solution provided by AtoZmath.com
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If alpha and beta are roots of quadratic equation, then find equation whose roots are alpha^2 and beta^2 calculator
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2. If `alpha` and `beta` are roots of equation
 1. `2x^2+3x-1=0`, find equation whose roots are `a/b,b/a`
2. `2x^2+3x-1=0`, find equation whose roots are `a/b^2,b/a^2`
3. `2x^2+3x-1=0`, find equation whose roots are `a^2+2,b^2+2`
4. `2x^2+3x-1=0`, find equation whose roots are `a+1,b+1`
5. `2x^2+3x-1=0`, find equation whose roots are `a^2b,b^2a`
6. `2x^2+3x-1=0`, find equation whose roots are `2a+3b,3a+2b`
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Example1. If `alpha` and `beta` are roots of quadratic equation `2x^2+3x-1=0`, then form the equation whose roots are `alpha/beta,beta/alpha`Solution:`2x^2+3x-1=0` Comparing the given equation with `ax^2+bx+c=0` We get `a=2,b=3,c=-1` Sum of roots `=alpha+beta=(-b)/a=(-3)/2` Product of roots `=alpha*beta=c/a=(-1)/2` Now, find equation whose roots are `alpha/beta,beta/alpha` Sum of roots `=(alpha/beta)+(beta/alpha)` `=(alpha^2+beta^2)/(betaalpha)` `alpha^2+beta^2=13/4`
We know that
`alpha^2+beta^2=(alpha+beta)^2-2alphabeta`
`:.alpha^2+beta^2=((-3)/2)^2-2*(-1)/2`
`:.alpha^2+beta^2=9/4+1`
`:.alpha^2+beta^2=13/4`
`betaalpha=(-1)/2` `:.(alpha^2+beta^2)/(betaalpha)=(13/4)/((-1)/2)=(-13)/2` `:.` Sum of roots `=(-13)/2` Product of roots `=(alpha/beta)*(beta/alpha)=1` `:.` Required equation is `x^2-((-13)/2)x+1=0` `:.2x^2+13x+2=0`
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