Find the roots of the quadratic polynomials?

Question

X-6x^2+1 

And 

6x-7x^2+6

 

 

Answer 1

1).

The quadratic polynomial is x - 6x² + 1.

The related quadratic equation is - 6x² + x + 1 = 0.

Compare the above equation with standard form of quadratic equation ax² + bx + c = 0.

a = - 6, b = 1, and c = 1.

To find the roots, substitute the values of a = - 6, b = 1, and c = 1 in Quadratic formula x = [ - b ± √ (b² - 4ac) ] / 2ab² - 4ac) ] / 2a.

x = [ - 1 ± √ (1² - 4 * (- 6) * 1 ) ] / 2 * (- 6).

x = [ - 1 ± √ (1 + 24 ) ] /(- 12)

x = - [ - 1 ± √25 ] /12

x = - [ - 1 ± 5 ] /12

x = - [ - 1 + 5 ] /12 and x = - [ - 1 - 5 ] /12

x = - 4 /12 and x = 6 /12

x = - 1/3 and x = 1/2.

Therefore, the roots of the polynomial are x = - 1/3 and x = 1/2.

 

Answer 2

2).

The quadratic polynomial is 6x - 7x² + 6.

The related quadratic equation is - 7x² + 6x + 6 = 0.

Compare the above equation with standard form of quadratic equation ax² + bx + c = 0.

a = - 7, b = 6, and c = 6.

To find the roots, substitute the values of a = - 7, b = 6, and c = 6 in Quadratic formula x = [ - b ± √ (b² - 4ac) ] / 2ab² - 4ac) ] / 2a.

x = [ - 6 ± √ (6² - 4 * (- 7) * 6 ) ] / 2 * (- 7)

x = [ - 6 ± √(204) ] / (-14)

x = (- 3 + √51) / (-7) and x = (- 3 - √51) / (-7)

x = (3 - √51) / 7 and x = (3 + √51) / 7

x = - 0.59 and x = 1.448775.

Therefore, the roots of the polynomial are x = - 0.59 and x = 1.45.