Question

Find all the values of k so that the quadratic expression factors into two binomials. Explain the process used to find the values.

5x2+kx-8

Answer 1

Explanation:

quadratic expression is,

5x² + kx - 8

quadratic formula is,

x = -b ± √b² - 4*a*c / 2*a

= -k ± √k² - 4*5*-8 / 2*5

= -k ± √k² + 160 / 10

= -k ± √k² + 13² / 10

= -k ± (k+13) / 10

= -k + k +13 / 10, -k - k - 13 / 10

= 13/10, -2k - 13/10

thus, x = 13/10 or x = -2k - 13 / 10

10x = -2k - 13

10x + 13 = -2k

k = 10x + 13 / -2

by substituting the value of x,

k = 10(13/10) + 13 / -2

= 13+13 / -2

=-26/2 = -13