If alpha and beta are roots of quadratic equation, then find alpha^2+beta^2 calculator

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1. If $alpha$ and $beta$ are roots of quadratic equation $2x^2-3x-6=0$ , then find $alpha^2+beta^2$

$alpha,beta$ are roots of ,

then find the value of

SolutionHelp

If alpha and beta are roots of quadratic equation, then find alpha^2+beta^2 calculator

1. If $alpha$ and $beta$ are roots of equation

$3x^2+8x+2=0$ , find

$a^2+b^2$

$3x^2+8x+2=0$ , find

$a-b$

$3x^2+8x+2=0$ , find

$a^3+b^3$

$3x^2+8x+2=0$ , find

$a/b^2+b/a^2$

$3x^2+8x+2=0$ , find

$ab^2+ba^2$

$3x^2+8x+2=0$ , find

$a/b+b/a$

Example

1. If $alpha$ and $beta$ are roots of quadratic equation $3x^2+8x+2=0$ , then find the value of $alpha^2+beta^2$

Solution:

$3x^2+8x+2=0$

Comparing the given equation with

$ax^2+bx+c=0$

We get

$a=3,b=8,c=2$

Sum of roots

$=alpha+beta=(-b)/a=(-8)/3$

Product of roots

$=alpha*beta=c/a=2/3$

Now we have to find

$alpha^2+beta^2$

$alpha^2+beta^2=52/9$

We know that

$alpha^2+beta^2=(alpha+beta)^2-2alphabeta$

$:.alpha^2+beta^2=((-8)/3)^2-2*2/3$

$:.alpha^2+beta^2=64/9-4/3$

$:.alpha^2+beta^2=52/9$

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