Question

let x1 x2 and x3 be the solutions of the equation 2x^3-x^2+2x-5 x=0 without solving the equations find the sum of the reciprocal value of the solutions of the given.equations​

Answer 1

Given :- let x1 x2 and x3 be the solutions of the equation 2x^3-x^2+2x-5 x=0 without solving the equations find the sum of the reciprocal value of the solutions of the given equations ?

Answer :-

we know that, for a cubic polynomial ax³ + bx² + cx + d = 0 ,

• Product of zeros = (-d/a)
• if we assume zeroes as p,q and r , then, sum of the product of zeroes taken two at a time = pq + qr + rp = c/a .

so, comparing given cubic polynomial 2x^3-x^2+2x-5 = 0 with ax³ + bx² + cx + d we get,

• a = 2
• b = (-1)
• c = 2
• d = (-5) .

then,

→ 1/x1 + 1/x2 + 1/x3

→ (x2*x3 + x1*x3 + x1*x2)/x1*x2*x3

→ (product of zeroes taken two at a time) / Product of zeros

→ (c/a) / (-d/a)

→ (c/a) * (a/-d)

→ (-c/d)

→ (-2/-5)

→ (2/5) (Ans.)

Learn more :-

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