1. Questions

Math

Prove that if the diffrence between the root of the equation ax^2+bx+c=0 is 1, then a=b^2-a^2/4c

  1. 👍
  2. 👎
  3. 👁
Skyboy

  1. the roots would be
    (-b +√(b^2 - 4ac)/2a and (-b - √(b^2 -4ac)/2a

    we are told that the difference between them is 1
    so,
    (-b+√(b^2-4a))/2a - (-b - √(b^2-4ac)/2a = 1
    2√(b^2-4ac)/2a = 1
    √(b^2 - 4ac) = a
    square both sides
    b^2 - 4ac = a^2
    b^2 - a^2 = 4ac
    divide both sides by 4c and we have our result

    (b^2 - a^2)/4c = a

    1. 👍
    2. 👎
    Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Alegbra 2

    Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with

  2. Math ~CHECK MY ANSWER~

    1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? a. Square root 120 , n , Square root 3

  3. ALGEBRA

    1, Factor each expression x^2 - 10x - 24 A. (x + 4)(x - 6) B. (x + 6)(x - 4) C. (x + 2)(x - 12) D. (x + 12)(x - 2) 2, x^2 - 36 = 0 A. (1 + square root of 3, 1 - square root of 3) B. (-6,6) C. No solution D. None of these 3, Factor

  4. maths

    prove that : 3^-3 * 6^2 * root 98 / 5^2 * cube root 1/25 * 15^-4/3 *3^1/3 is equal to 28 root 2

  1. maths

    If a+ib = (root of 1+i) / (root of 1-i )then prove a^2 +b^2 =1

  2. Geometry

    Martin wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram ABCD in the coordinate plane so that A is (0, 0), B is (a, 0), C is (a, b), and D is (0, b). What

  3. math

    solve the equation below algebraically and express the result in simplest radical form 13/x=10-x I did 13/x=10-x multiplied each side by x and then subtracted 13 to get 0=13-(10x-x^2) x^2-10x+13=0 x=(10+/- square root of 100-52)/2

  4. calculus

    3x4 − 8x3 + 5 = 0, [2, 3] (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x4 − 8x3 + 5. The polynomial f is continuous on [2, 3], f(2) = < 0, and f(3) = > 0, so by the

  1. Algebra

    Use the quadratic formula to solve the equation. Give exact answers: 2x^2 -1 = 6x. The choices are: a) -3 + square root(7)/2, -3 - square root(7)/2 b) 3 + square root(11)/2, 3 - square root(11)/2 c) 3 + square root(7)/2, 3 -

  2. Algebra 2a

    Help please! 1. What are the real or imaginary solutions of the polynomial equation? x^4-52x^2+576=0 A) 4,-4 B) 4,-6 C) 4,-4,6,-6 D) no solutions 2. What are the real or imaginary solutions of the polynomial equation? x^3=216 A)

  3. Math Help!

    Four students worked to find an estimate for square root 22. Who is closest to finding the true estimate? A. Tiffany: "Use square root 16 and square root 25 to estimate." B. Todd: "I use square root 9 and square root 16." C.

  4. math

    Four students work to find an estimate for square root 37. Who is closest to finding the true estimate? (1 point) Rhonda: "Use square root 16 and square root 25 to estimate." Ricardo: it should be between square root 25 and square

You can view more similar questions or ask a new question.