Question

Which are the solutions of the quadratic equation? x2 = 9x + 6 StartFraction negative 9 minus StartRoot 105 EndRoot Over 2 EndFraction comma StartFraction negative 9 + StartRoot 105 EndRoot Over 2 EndFraction StartFraction negative 9 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFraction negative 9 + StartRoot 57 EndRoot Over 2 EndFraction StartFraction 9 minus StartRoot 105 EndRoot Over 2 EndFraction comma StartFraction 9 + StartRoot 105 EndRoot Over 2 EndFraction StartFraction 9 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFraction 9 + StartRoot 57 EndRoot Over 2 EndFraction

Answer 1

x = 9+√105/2 or 9-√105/2

Explanation:

Given the quadratic function x² = 9x+6

Re arranging we have;

x²-9x-6 = 0

Comparing this equation to general form ax²+bx+c = 0;

a = 1, b = -9, c = -6

Using the general formula to find x.

x = -b±√b²-4ac/2a

x = -(-9)±√81-4(1)(-6)/2

x = 9±√81+24/2

x = 9±√105/2

x = 9+√105/2 or 9-√105/2

Answer 2

The correct answer is C. 9 -√ 105/ 2, 9 + √ 105/ 2

Explanation:

Let's find the solutions for the quadratic equation:

x² = 9x + 6

x² - 9x -6 = 0

Using the quadratic formula, we have:

x = [- (-9) +/- √ (-9)² - 4 * 1 * -6]/2 * 1

x = [ 9 +/- √ (81 + 24]/2

x = [ 9 +/- √ (105]/2

x₁ = [ 9 + √ (105]/2

x₂ = [ 9 - √ (105]/2

The correct answer is C. 9 -√ 105/ 2, 9 + √ 105/ 2

Note: Same answer than question 14133688, answered by me today.