Question

The parabola y = x² + px + q cuts the straight line y = 2x – 3 at a point with abscissa 1 then the values of p and q for which the distance between the vertex of the parabola and the x- axis is the minimum, is-

• A. p = –1, q = –1
• B. p = –2, q = 0
• C. p = 0, q = –2
• D. p = – $\frac{3}{2}$, q = –$\frac{1}{2}$

Answer 1

Answer: (B)

p = –2, q = 0

Answer 2

y = 2 – 3 ̃ y = –1 ̃ Point (1, –1)

– 1 = 1 + p + q ̃ p + q = –2 ... (i)

distance between vertex and x axis = $\frac{p^{2}}{4}$– q

= $\frac{p^{2}}{4}$+ p + 2

= $\frac{1}{4}$ ((p + 2)² + 4)

for minimum p = –2

Hence q = 0