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Lesson 76

Lesson 76. Finding polynomial roots. Polynomial roots. Polynomial roots are the solutions of a polynomial equation. These roots are the zeros of the related polynomial function which are the x-intercepts of the graph of the function. Finding roots of a factored polynomial.

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Lesson 76

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  1. Lesson 76 Finding polynomial roots

  2. Polynomial roots • Polynomial roots are the solutions of a polynomial equation. • These roots are the zeros of the related polynomial function which are the x-intercepts of the graph of the function.

  3. Finding roots of a factored polynomial • Find the roots of: • 0 = 2x(x-5)(2x-3) • 2x = 0 x-5 = 0 2x-3 = 0 • x= 0 x = 5 x = 3/2 • Find the roots of: • 0 = -x (x+4)(x- 1/2)

  4. Finding monomial factors to determine zeros • Find the zeros of the polynomial function: • f(x) = 6x3 + 10x2 + 4x • factor GCF 2x(3x2 + 5x +2) • So 2x= 0 , x= 0 • factor 3x2 + 5x +2 using quadratic formula • so zeros are 0, -2,-3

  5. Find the zeros • f(x) = 6x3 + 21x2 + 18x • f(x) = x4 - 3x3 + 2x2 - 6x

  6. Finding binomial factors to determine roots • Find real roots of • 0 = (x+3)(x2+4)-(x+3)(4x+1) • Common factor • 0 = (x+3)(x2+4-(4x+1)) • 0 = (x+3)(x2 -4x +3) • 0 = (x+3)(x-3)(x-1) • So x + 3 = 0 x - 3 = 0 x - 1 = 0 • x = -3 x = 3 x = 1

  7. Find real roots • (x-2)(x2 +2)-(x-2)(4x+7)= 0 • 0 = (x-7)(3x3+4)+(x-7)(5x2 -1) • 0 = (x+4)(2x3 -7)+ (x+4)(5-3x)

  8. Solving polynomial equations • 5x4 = 5x3 - 8x2 -2x • 2x4 = 8x3 - x2 - 13x

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