Question

Show that the equation 3x² + 7x + 8 = 0 is not true for any real value of x.

[Hint: D = (49 – 4 × 3 × 8) = (49 – 96) = – 47 < 0.]

Answer 1

Given: 3x² + 7x + 8 = 0

Step-wise calculation:

1. Compare with ax² + bx + c = 0:

a = 3, b = 7, c = 8

2. Discriminant D = b² − 4ac

= 7² – 4 × 3 × 8

= 49 – 96

= –47

3. D < 0, so the quadratic has no real roots (the roots are imaginary).

Since the discriminant is negative, 3x² + 7x + 8 = 0 has no real solution; the equation is not true for any real value of x.