Polynomial roots

Find the other zeroes of the polynomial 2x⁴+3x³-3x²-6x-2, if two of them are root2 & -root2

Correct answer:

x₃ =  -0.5
x₄ =  -1

Step-by-step explanation:

$$\begin{gathered} x_1=\sqrt{2}=\sqrt{2}\doteq 1.4142 \\ {x}_2=-\sqrt{2}=-\sqrt{2}\doteq -1.4142 \\ (x-x_1)(x-x_2)=x^2-2 \\ 2x^4+3x^3-3x^2-6x-2=(x^2-2)(2x^2+3x+1) \\ 2z^2+3z+1=0 \\ 2z^2+3z+1=0 \\ 2z^2+3z+1=0 \\ a=2;b=3;c=1 \\ D=b^2-4ac=3^2-4\cdot 2\cdot 1=1 \\ D>0 \\ {z}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-3\pm \sqrt{1}}{4}} \\ {z}_{1,2}={\displaystyle \frac{-3\pm 1}{4}} \\ {z}_{1,2}=-0.75\pm 0.25 \\ {z}_1=-0.5 \\ {z}_2=-1 \\ \text{ Factored form of the equation: } \\ 2(z+0.5)(z+1)=0 \\ {x}_3=z_1=(-0.5)=-0.5 \end{gathered}$$

Our quadratic equation calculator calculates it.

$x_4=z_2=(-1)=-1$

Try another example

Related math problems and questions:

• Roots
  Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
• Roots and coefficient
  In the equation 2x ^ 2 + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b.
• Root
  Use law of square roots roots: ?
• Square roots
  What is equal to the product of the square roots of 295936?
• Three members GP
  The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
• Biquadratic
  By introducing a new variable solve biquadratic equation: ?
• Root
  The root of the equation (x-19)² -10 = x² -11x is (equal or greater or less than zero)? ...
• Quadratic equation
  Determine the numbers b, c that the numbers x₁ = -1 and x₂ = 3 were roots of quadratic equation: -3x ² + b x + c = 0
• Equation
  Equation -2x²+bx -82 =0 has one root x₁ = -8. Determine the coefficient b and the second root x₂.
• Quadratic equation
  Find the roots of the quadratic equation: 3x²-4x + (-4) = 0.
• Quadratic equation
  Quadratic equation 7x²+bx+c=0 has roots x₁ = 67 and x₂ = -84. Calculate the coefficients b and c.
• Quadratic equation
  Solve quadratic equation: 2x²+28x-550=0
• Find the 20
  Find the product and the sum of the roots of x² + 3x - 9 = 0
• Pure quadratic equation
  Solve pure quadratic equation -5x² +10 = 0.
• Square root 2
  If the square root of 3m² +22 and -x = 0, and x=7, what is m?
• Find parameters
  Find parameters of the circle in the plane - coordinates of center and radius: ?
• Completing square
  Solve the quadratic equation: m²=4m+20 using completing the square method