2xsquared-9x+1=0 value of discriminant and number of real solutions

• discriminant: 73

• # of real solutions: 2

Step-by-step explanation:

Comparing the equation ...

2x^2 -9x +1 = 0

to the generic form ...

ax^2 +bx +c = 0

we find the coefficient values to be ...

a = 2; b = -9; c = 1

That makes the value of the discriminant, (b^2 -4ac), be ...

(-9)^2 -4(2)(1) = 81 -8 = 73

Since the discriminant is positive, the number of real solutions is 2.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right