Question

To find the solutions to an equation of the form ax2+bx+c , use the quadratic equation: x=−b±b2−4ac√2a . What are the two solutions to 2x2−x−4=0 ? Use the quadratic equation. (Report the greater of the two solutions first, using 3 significant digits for both solutions)

Answer 1

Brahmagupta’s solution to a quadratic equation of the form ax2 + bx = c involved only one solution. Which solution would he have found for the equation 3x2 + 4x = 6?

first option.

To find the solutions to an equation of the form ax2+bx+c , use the quadratic equation: x=−b±b2−4ac√2a . What are the two solutions to 2x2−x−4=0 ? Use the quadratic equation. (Report the greater of the two solutions first, using 3 significant digits for both solutions)

third option.

Answer 2

1.686

Explanation:

Given is an quadratic equation as

`2x^2-x-4=0`

Also we are given the formula for general equation

`ax^2+bx+c` as

`(-b+/-√(b^2-4ac) )/(2a)`

Here in our equation we have

`a=2\\b=-1\\c=-4`

Hence solution would be

`(1+√(1+32) )/(4) ,(1-√(1+32) )/(4) \\(1+√(33) )/(4) ,(1-√(33) )/(4)`

Greater would be the one with positive square root

`(1+√(33) )/(4) \\=1.6861\\=1.686`