Solve the quadratic equation 2x² − 5x − 4 = 0. Give your answers correct to three significant figures.

The nature of the roots of the equation 3x² − 6x − 3 = 0 is: (a) Real and equal (b) Real, distinct and rational (c) Real, distinct and irrational (d) No real roots

Solve the following quadratic equation for x and give your answers correct to three significant figures: 2x² − 10x + 5 = 0

Solve the quadratic equation (x − 2)² − 5x − 3 = 0 and give your answer correct to 3 significant figures.

Mr and Mrs Das travelled by car from Delhi to Kasauli, a distance of approximately 350 km. Heavy rain reduced the average speed by 20 km/h and increased the journey time by 2 hours. Find: (a) the original speed of the car. (b) the time taken at the reduced speed.

The roots of the equation px² − qx + r = 0 are real and equal if: (a) p² = 4qr (b) q² = 4pr (c) −q² = 4pr (d) p² > 4qr

If 3 is a root of the quadratic equation x2 − px + 3 = 0, then p is equal to: (a) 4 (b) 3 (c) 5 (d) 2

The difference of two natural numbers is 5 and sum of their reciprocals is . Find the two numbers.

A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more, it would have taken 1 hour less. Find x, the original speed.

Solve the following quadratic equation: x2 + 4x − 8 = 0. Give your answer correct to one decimal place. Use mathematical tables if necessary.

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is: (a) 30° (b) 60° (c) 90° (d) 120°

The factor common to the two polynomials x² − 4 and x³ − x² − 4x + 4 is: (a) (x + 1) (b) (x − 1) (c) (x − 2) (d) (x − 4)