QQuestion
Solve the following quadratic equation for x and give your answers correct to three significant figures:
2x² − 10x + 5 = 0
✓Answer
Comparing 2x² − 10x + 5 = 0 with ax² + bx + c = 0:
a = 2, b = −10 and c = 5
Using the quadratic formula:
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}Substituting the values:
x=\frac{-(-10)\pm\sqrt{(-10)^2-4(2)(5)}}{2(2)}⇒ x=\frac{10\pm\sqrt{100-40}}{4}
⇒ x=\frac{10\pm\sqrt{60}}{4}
⇒ x=\frac{10\pm2\sqrt{15}}{4}
⇒ x=\frac{5\pm\sqrt{15}}{2}
Since √15 ≈ 3.87298:
x = (5 + 3.87298)/2 or x = (5 − 3.87298)/2
⇒ x ≈ 4.43649 or x ≈ 0.563508
Correct to three significant figures:
x = 4.44 or x = 0.564
Related Questions
More ICSE Moderate level questions
Solve the quadratic equation 2x² − 5x − 4 = 0. Give your answers correct to three significant figures.
The quadratic equation 3x² + √7x + 2 = 0 has: (a) two equal real roots. (b) two distinct real roots. (c) more than two real roots. (d) no real roots.
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
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.
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
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.
Mr Gupta invested ₹33,000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%. Find: (a) the number of shares purchased by him. (b) his annual dividend.
The letters A, D, M, N, O, S, U and Y of the English alphabet are written on separate cards and put in a box. The cards are well shuffled and one card is drawn at random. What is the probability that the card drawn is a letter: (a) of the word MONDAY? (b) which does not appear in MONDAY? (c) which appears both in SUNDAY and MONDAY?
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 − n). Find: (a) its first term and common difference. (b) the sum of its first 25 terms.
(a) If the lines kx − y + 4 = 0 and 2y = 6x + 7 are perpendicular to each other, find the value of k. (b) Find the equation of a line parallel to 2y = 6x + 7 and passing through (−1, 1).
Rohan bought the following eatables for his friends: S. No. Item Price Quantity Rate of GST 1 Laddu ₹500 per kg 2 kg 5% 2 Pastries ₹100 per piece 12 pieces 18% Calculate: (a) the total GST paid. (b) the total bill amount including GST.