Question

sum of reall roots of 2x⁴-7x³+9x²-7x+2=0​ is

Answer 1

Answer:

Please see the attachment

Answer 2

sum of real roots = 5/2

we have to find sum of real roots of 2x⁴ - 7x³ + 9x² - 7x + 2 = 0

let's arranging to find roots .

putting, x = 2

2(2)⁴ - 7(2)³ + 9(2)² - 7(2) + 2

= 32 - 56 + 36 - 14 + 2

= 70 - 70 = 0

so, x = 2 is a root of given expression.

then, 2x⁴ - 4x³ - 3x³ + 6x² + 3x² - 6x - x + 2 = 0

⇒2x³(x - 2) - 3x²(x - 2) + 3x(x - 2) -1(x - 2) =0

⇒(x - 2)(2x³ - 3x² + 3x - 1) = 0

⇒(x - 2){2x³ - x² - 2x² + x + 2x - 1} = 0

⇒(x - 2){x²(2x - 1) -x(2x - 1) + 1(2x - 1)} = 0

⇒(x - 2)(2x - 1){x² - x + 1} = 0

so, we have x = 2 , 1/2 but x² - x + 1 ≠ 0 [because discriminant , D = (-1)² - 4(1) < 0]

hence, we have two real roots i.e., 2, 1/2

then, sum of real. roots = 2 + 1/2 = 5/2

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