Question

Wielomiany! PROSZE O POMOC.Pytania w zalaczniku

Answer 1

W(x) = x³-7x+6

W(-2) = (-2)³-7(-2)+6 = -8+14+6 = 12  ≠ 0  

W(-1) = (-1)³-7(-1)+6 = -1+7+6 = 12  ≠ 0

W(1) = 1³-7·1+6 = 1-7+6 = 0   => x = 1

W(2) = 2³-7·2+6 = 8-14+6 = 0  => x = 2

Odp. Pierwiastki tego wielomianu: 1;2

 

a)

W(x) = x⁴+3x³+8x²+18x+12

W(-2) = (-2)⁴+3(-2)³+8(-2)²+18(-2)+12 = 16-24+32-36+12 = 0   => x = -2

W(-1) = (-1)⁴+3(-1)³+8(-1)²+18(-1)+12 = 1-3+8-18+12 = 0   => x = -1

W(1) = 1⁴+3·1³+8·1²+18·1+12 = 1+3+8+18+12 = 42  ≠ 0

W(2) = 2⁴+3·2³+8·2²+18·2+12 = 16+24+32+16+12 = 100  ≠0

Odp. Pierwiastki tego wielomianu: -2;-1

 

b)

W(x) = x³+5x²+2x-32

W(-2) = (-2)³+5(-2)²+2(-2)-32 = -8+20-4-32 = -24  ≠ 0

W(-1) = (-1)³+5(-1)²+2(-1)-32 = -1+5-2-32 = -30  ≠ 0

W(1) = 1³+5·1²+2·1-32 = 1+5+2-32 = -24  ≠ 0

W(2) = 2³+5·2²+2·2-32 = 8+20+4-32 = 0   => x = 2

Odp. Pierwiastkiem tego wielomianu jest: 2

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1.

W(x) = (3x-4)(7-2x)(4-2x)

(3x-4)(7-2x)(4-2x) = 0

3x-4 = 0   => x = 1⅓

lub

7-2x = 0   => x = 3½

lub

4-2x = 0   => x = 2

Odp. x = 1½   v   x = 2   v   x = 3½

 

2.

W(x) = (x²-4)(2x-1)(x-½)

(x²-4)(2x-1)(x-½) = 0

(x+2)(x-2)·2(x-½)(x-½) = 0

2(x+2)(x-2)(x-½)² = 0

x+2 = 0   => x = -2

lub

x-2 = 0   => x = 2

lub

x-½ = 0   => x = ½

Odp. x = -2   v   x = ½   v   x = 2