Polynomial Equation - Roots Formulas

Important

If $$A_{n}X^{n}$$ + $$A_{n-1}X^{n-1}$$ + ... + $$A_{1}X$$ + $$A_{0}$$ = 0 and n>=3, then 

  • Sum of the roots = $$-A_{n-1}/ A_{n}$$

  • Sum of roots taken two at a time = $$A_{n-2}/ A_{n}$$

  • Sum of roots taken three at a time = $$-A_{n-3}/ A_{n}$$ and so on

  • Product of the roots =$$(-1)^nA_0/A_n$$

Ex: For a cubic ax³+bx²+cx+d=0 with roots p,q,r:

  • p+q+r = −b/a

  • pq+qr+rp = c/a

  • pqr = −d/a

Question 1

Amrit solves a quadratic equation but notes the constant term wrong and gets the roots as (9,4) while Nag notes the coefficient of x wrong and gets the roots as (6,2). What are the correct roots of the original equation?

Question 2

If x and y are the roots of the equation $$a^{2} - 5a -1 =0$$. What is the value of (4+x)*(4+y)?

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Polynomial Equation - Roots Formulas

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