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(a) The first four Hermite polynomials are $1, 2t,-2+4t^2,$ and $-12t+8t^3$. These polynomials arise naturally in the study of certain important differential equations in mathematical physics. Show that the first four Hermite polynomials form a basis of $\mathbb{P}_3$.
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Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0. t=\frac{-4±\sqrt{4^{2}-4\times 3}}{2}
Examples. \left. \begin {cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end {cases} \right. Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.
t=\frac{-3±\sqrt{3^{2}-4\times 4\left(-1\right)}}{2\times 4} This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 3 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
