The first formula found for solving cubic equations applied only to cubics without a square term. In modern notation, these look like x³ + px + q = 0. These are sometimes called "depressed cubics." Let y = x - and substitute in the equation below to "reduce" the cubic. Verify that the square term will disappear. y³ + ay² +by+c=0

Q: If the roots of the equation a(b - c)x² +b(c - a)x + c (a - b) = 2 11 are equal, show that ==±+:

A: We can use properties of square of three no. To solve the problem

Q: 2. Solve each equation. Identify any extraneous roots: a) (x+3)2 – 1=X -1= x b) V3x +13 = X +5 c)…

A:

Q: Show that the product of the roots of a quadratic equation is c/a .

A: Consider the quadratic equation ax2+bx+c=0 Also consider that α and β are the roots of the quadratic…

Q: If the sum of the roots of the equation 1/(x+ a) + 1/(x + b) = 1/c is zero, then prove that the…

A:

Q: Find the fourth roots for the equation z4-2z²+4=0

A:

Q: equation 1.    x² – 5x + 9 = 0  2.     x² – 2x = –10    3.     9x² + 6x + 1 = 0

A:

Q: x² +24x = 16 (Burton)

A:

Q: Solve −5x^2−13x+1=0 for x by using the quadratic formula or otherwise. Enter each solution in surd…

A: To solve quadratic equation,  −5x^2−13x+1=0 Using quadratic formula and represent solutions in surd…

Q: 2. Explain how finding cube roots by paper folding is just a special case of the method to find…

A: The fold-and-cut problem asks what shapes can be obtained by folding a piece of paper flat and…

Q: Suppose x = a, e are two solutions to the cubic equation x³ + px = q . Use Viete's approach to find…

A:

Q: Find the positive root of the equation 4x2 – 36 = 0.

A: We can find the answer as given below

Q: Find the depressed cubic equations for x3 - 6x2 -24x + 64 = 0

A: Given, x3-6x2-24x+64=0                   .......1Here, a=1 , b=-6 , c=24 , d=64Put x…

Q: an you detail step by step how did you resolve the cubic equation

A: We have cubic equation σp3-48σp2-2184σp+38320=0 To solve a cubic equation we find one root using hit…

Q: Determine the roots of the following quadratic expression 4x² - 19x + 12 = 0 a) x=3 and x=-16 b) x =…

A:

Q: 29. Use the quadratic formula to find the roots of the following quadratic: y = 2x² – 11x + 5 -

A:

Q: Answer the following: 1. Characterize the roots of the following quadratic equations using the…

A:

Q: If the roots of a quadratic equation: A x 2 + B x + C = 0 are x=5 and x=4/3, then what is the…

A: Consider the given quadratic equation: Ax2+Bx+C=0 Root of the above equation is x=5 and x=43 Here,…