Question

. If a and B are zeros of polynomial 3.x2 + 2x - 6, then find the value
of: () a-B, (ii).a2 + B2, (ii) a + B. (iv) -+a
a
6​

Answer 1

Step-by-step explanation:

Given quadratic eq. $3x^{2} +2x-6$

by this we can get

a+b= -2/3    a*b= -2

let a=$\alpha$ and b=$\beta$

a^2=$\alpha^{2}$         b^2=$\beta^{2}$

a)

(a+b)^2=4/9

a^2+b^2+2*a*b=4/9

(a-b)^2+4*a*b=4/9

(a-b)^2+4*(-2)=4/9

(a-b)^2=4/9+8

(a-b)^2=76/9

a-b=$\sqrt{76/9}$

**   a-b=$\sqrt{76}/3$

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b) (a+b)^2=4/9

    a^2+b^2+2*a*b=4/9

    a^2+b^2+2*(-2)=4/9

    a^2+b^2=4/9+4

**     a^2+b^2=40/9

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c) w.k.t a^3+b^3=(a+b)*($a^{2}+b^{2}-ab$)

   a^3+b^3= (-2/3)*(40/9-(-2))

   a^3+b^3= (-2/3)*(58/9)

**      a^3+b^3= -116/27

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d) 1/a+1/b=a+b/ab

                =(-2/3)/-2

    1/a+a/b=1/3