Question

For what value of a the curve y = x² + ax + 25 touches the x - axis

• A. 0
• B. ±5
• C. ±10
• D. None of these

Answer 1

Answer: (C)

±10

Answer 2

For the quadratic curve to touch the x-axis, the discriminant must be zero. For

$$y = x^2 + ax + 25,$$

the discriminant is

$$\Delta = a^2 - 4 \times 1 \times 25 = a^2 - 100.$$

Setting $\Delta = 0$:

$$a^2 - 100 = 0 \implies a^2 = 100 \implies a = \pm 10.$$