Find all rational zeros of the polynomial, and then find the irrational zeros, if any. Whenever appropriate, use the Rational Zeros Theorem, the Upper and Lower Bounds Theorem, Descartes

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Supoilign1964 · Accepted Answer

Step 1 Zeros of the polynomial are those values which return zero value for the function when put in place for independent variable. Zeroes of a polynomial are values for which function f(x) returns value 0. Highest power of polynomial is the degree of the polynomial. Degree of polynomial is the highest power that the polynomial has. Leading coefficient is the coefficient of the term in polynomial which has highest power. X-intercept is the point where graph of polynomial function touches/crosses x-axis, i.e y=0 . Y-intercept is the point where graph of polynomial function touches/crosses y-axis-axis, i.e x=0 Step 2 We can simplify the given polynomial as P(x)=2x4+3x3−4x2−3x+2 By trial and error we can find that P(1)=0, hence (x-1) is factor of the polynomial. P(x)=(x−1)(2x3+5x2+x−2) Again by trial error we can find, P(-1)=0, hence (x+1) is also factor of above polynomial P(x)=(x−1)(x+1)(2x2+3x−2) Solving the quadratic, we get P(x)=(x−1)(x+1)(2x−1)(x+2) Hence the rational zeros of the polynomial are x=1,-1,1/2,-2. Polynomial has no irrational zeros.

Find all rational zeros of the polynomial, and then find

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