Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
16x2 = 24x + 1
Given: 16x2 = 24x + 1
16x2 – 24x – 1 = 0
Comparing with standard quadratic equation ax2 + bx + c = 0
a = 16, b = – 24, c = – 1
Discriminant D = b2 – 4ac
= (– 24)2 – 4.16. – 1
= 576 + 64 = 640 > 0
Hence the roots of equation are real.
Roots are given by
Hence the roots of equation are