Solve x ^ 4 - 17x ^ 2 + 16 = 0 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x^{4}-17x^{2}+16=0$$

Solve for x

$x=-4$
$x=4$
$x=1$
$x=-1$

Steps Using the Quadratic Formula

Substitute $t$ for $x^{2}$.

$$t^{2}-17t+16=0$$

All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. Substitute $1$ for $a$, $-17$ for $b$, and $16$ for $c$ in the quadratic formula.

$$t=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 1\times 16}}{2}$$

Do the calculations.

$$t=\frac{17±15}{2}$$

Solve the equation $t=\frac{17±15}{2}$ when $±$ is plus and when $±$ is minus.

$$t=16$$ $$t=1$$

Since $x=t^{2}$, the solutions are obtained by evaluating $x=±\sqrt{t}$ for each $t$.

$$x=4$$ $$x=-4$$ $$x=1$$ $$x=-1$$