Question

Determine the nature of roots of the quadratic equation 2x^-5x+7

Answer 1

Solution:

$2 {x}^{2} - 5x + 7 = 0 \\ therefore \: d = { (- 5)}^{2} - 4 \times 2 \times 7 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 25 - 56 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 31 \\ as \: the \: value \: of \: d \: is \: negative \: therefore \: the \: roots \: are \: real \: and \: imaginary$

Answer 2

b^2-4ac
(-5)^2-4*2*7
25-56
-31
Hence the roots are imaginary