trig

posted by .

How do you write the quadratic equation with integer coefficients that have the roots 7-3i and 7+3i?

  • trig -

    In the quadratic equation
    ax²+bx+c=0
    b/a = -(sum of the two roots)
    c/a = product of the two roots.

    Assume a=1, then
    b=-(7-3i+7+3i)=-14
    c=(7-3i)*(7+3i)=49+9=58
    So the quadratic equation is
    x²-14x+58=0

    Check by solving the equation and you should get back 7±3i as the roots.

  • trig -

    x = 7 + 3i, and X = 7 - 3i.

    We can use either of the 2 values of X:
    X = 7 + 3i,
    (X - 7) = 3i,
    Square both sides:
    X^2 --14X + 49 = 9(-1),
    X^2 - 14X + 49 +9 = 0,
    X^2 - 14X + 58 = 0.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra2

    Find the polynomials roots to each of the following problems: #1) x^2+3x+1 #2) x^2+4x+3=0 #3) -2x^2+4x-5 #3 is not an equation. Dod you omit "= 0" at the end?
  2. Algebra

    Find a quadratic equation with integer coefficients whose roots are 2 and7.
  3. Math

    1)Write a quadratic equation with integer coefficients that has -4+7i(Radical 3) and -4-7i(Radical 3) as its roots. 2) Solve your answer to part 1 using the quadratic formula verifying your answer
  4. Alg2

    Find a quadratic equation with integral coefficients having roots 1/2 and -5/2.
  5. Algebra

    Find the number of integer quadruples (a,b,c,d) with 0\leq a,b,c,d \leq 100, such that a and b are the roots of the quadratic equation x^2-cx+d=0, while c and d are the roots of the quadratic equation x^2-ax+b.
  6. Algebra

    Find the number of integer quadruples (a,b,c,d) with 0\leq a,b,c,d \leq 100, such that a and b are the roots of the quadratic equation x^2-cx+d=0, while c and d are the roots of the quadratic equation x^2-ax+b
  7. Math

    I can't remember how you find the roots of quadratic equations other than determining the zeroes of the equation and finding the x-intercepts. Can someone please give me a clear answer on this as my dad has been useless on this topic …
  8. Algebra

    If a quadratic equation with real coefficients has a discriminant of 225, the what type of roots does it have?
  9. algebra

    if a quadratic equation with real coefficients has a discrimiant of 225, then what type of roots doe it have?
  10. Algebra 2

    Q: Write a quadratic equation with integral coefficients whose roots are -6+i and -6-i My Answer: x^2+12x+37 (first) sum=-12 product=37 (then) write equation using formula x^2-(sum)x+product Is my work and answer correct?

More Similar Questions