solve the polynomial equation x 4 5x 2 36 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 5 for b and 36 for c in the quadratic formula
Substitute the POSSIBLE roots one by one into the polynomial to find the actual roots Start first with the whole numbers If we plug these values into the polynomial P x we obtain To solve a polynomial equation write it in standard form variables and canstants on one side and zero on the other side of the equation Factor it and set each factor to zero Solve each
solve the polynomial equation x 4 5x 2 36 0
solve the polynomial equation x 4 5x 2 36 0
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Divide x 4 5x 2 36 by x 3 to get x 3 3x 2 4x 12 To factor the result solve the equation where it equals to 0 12 6 4 3 2 1 By Rational Root Theorem all rational By Factor theorem x k is a factor of the polynomial for each root k Divide x 4 5x 2 36 by x 2 to get x 3 2x 2 9x 18 To factor the result solve the equation where it equals to 0
The first term is x4 its coefficient is 1 The middle term is 5x2 its coefficient is 5 The last term the constant is 36 Step 1 Multiply the coefficient of the first term by the constant 1 36 Step by step solution Step 1 Equation at the end of step 1 x 4 5x 2 36 0 Step 2 Step 3 Pulling out like terms 3 1 Pull out like factors 36 5x 2 x 4 x 4 36x4
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solve the polynomial equation x 4 5x 2 36 0 - Divide x 4 5x 2 36 by x 3 to get x 3 3x 2 4x 12 To factor the result solve the equation where it equals to 0 12 6 4 3 2 1 By Rational Root Theorem all rational