Question

find the value of the discriminant of the quadratic equation and comment on the nature of the roots. Solve the equation. 4x2 – 17x = 15 please show work.

Answer 1

b^2 - 4ac

a = 4
b = -17
c = -15

(-17)^2 - 4(4)(-15)
529

Answer 2

as the result we got is Positive so it means that we will have 2 real roots.

Answer 3

and since by some miracle 529 is a perfect square (it is the square of 23) your two solutions will be rationals as well

Answer 4

\[\sqrt{b ^{2}-4ac}\]
So we have \[4x^{2}-17x-15=0\]
\[\sqrt{(-17) ^{2}-4(4)(-15)}=529\]
529 = 23^2,
So there will be two rational roots.