Question

If αα,ββ are roots of 3x2−5x+7=03x2−5x+7=0 then α2α2+β2β2=


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Answer 1

Answer:

$\huge{\boxed{\rm{\red{α²+β²=-17/9}}}}$

Step-by-step explanation:

Given quadratic equation is 3x²-5x+7=0

On comparing with the standard quadratic equation ax² +bx+c=0

a=3;b=-5;c=7

If α,β are roots then

Sum of the roots =(α+β)=-b/a

=>α+β=-(-5)/3

=>α+β=5/3------>(1)

Product of the roots=(αβ)=c/a

=>αβ=7/3-------->(2)

we know that (a+b)²=a²+b²+2ab

=>a²+b²=(a+b)²-2ab

now

α²+β²=(α+β)²-2(αβ)

=>α²+β²=(5/3)²-2(7/3)

=>α²+β²=25/9-14/3

=>α²+β²=(25-42)/9

=>α²+β²=-17/9

The value of α²+β²=-17/9