Quadratic Equat...

The equation ax² + bx + c = 0 has equal roots. Based on this information, which of the following is correct?

If n = , then what is the value of n?

Which among the following is a root of the quadratic equation 17x² – 153x + 340 = 0?

How many positive integers will 'k' take, such that the roots of the quadratic equation 2x² - 13x + k = 0 are real?

If 3 is a real root of the equation x² + bx – 15 = 0 and equation x² + bx + q = 0 has equal roots, then what is the value of q?

What is the value of p - q, if the roots of the quadratic equation px² - (p + q)x + q = 0 are reciprocals?

If the roots of the quadratic equation ax² + bx + c = 0 are negative to each other, then

If one of the roots of 3x² + ax + 36 = 0 is thrice the other, then the value of a is ___.

_{The roots of the equation can be found by solving}

If the equation tx² + sx + u = 0 has equal roots, then what is the value of u?

If α and β are the roots of the equation 3x² + 4x + 7 = 0, then the value of is

What is the sum of the solutions of the equation 1 = ?

The product of two consecutive positive odd integers is 63, the smaller integer being x. Which of the following quadratic equations represents this situation?

Which of the following is the solution set of the quadratic equation ?

A positive number is increased by 16 and then squared. The resulting number is 368 more than twice the square of the original number. Which among the following is possibly the original number?

In a right-angled triangle ABC, the length of the longest side is 10 cm. The perpendicular of this triangle is 2 cm more in length than its base. If x represents the length of the perpendicular, then which of the following quadratic equations represents this case?

Rachel can cover a distance of 56 km at some constant speed in a certain time. If she increases her speed by 1 km/hr, she will be able to cover the same distance in an hour less. What would be the time taken by her to cover a distance of 104 km at the increased speed?

A boat covers 50 km upstream and 40 km downstream in total 7.5 hours. The speed of boat in still water is 15 km/hr. If the speed of stream is x km/hr, then which of the following quadratic equations correctly represents this case?

There are two squares. Side of one square measures 4 cm more in length than that of the other. The sum of their areas is 400 cm². Which among the following represents the area of the larger square?

A bought some notebooks. These notebooks cost him Rs. 300. After a few days, the cost of each notebook dropped by Rs. 5. At this price, he could buy 5 more notebooks for the same amount. What was the original cost of a notebook?

Which of the following equations does not have real roots?

Directions: Read the given statements carefully.

Statement I: The quadratic equation 108x² – 288x + 192 = 0 has real and equal roots.
Statement II: If the equation 18x² + 12kx + 8 = 0, where k > 0, has equal roots, then both the roots are equal to .

Which among the following is a factor of the polynomial 9x² + 63x + 108?

Directions: Determine whether the given statements are true (T) or false (F) and choose the correct option accordingly.

(i) is the solution set for the quadratic equation = (a + b)².


(ii) Two friends, A and B, are discussing their ages. The age of B is square of the age of A. B will be 3 times as old as A after 5 years. The difference between their current ages is 20 years.


(iii) Two taps, A and B, together can fill a tank in 10 hours. Tap A, which is bigger, can fill the tank in 16 hours less than tap B, which is smaller. If x is the number of hours required to fill the tank by the smaller tap, then this case can be represented by equation x² + 36x + 160 = 0.

(iv) The quadratic equation has the discriminant equal to 0.

There are two rectangles, ABCD and PQRS. ABCD lies inside PQRS such that there is a uniform width all around ABCD. The difference between the areas of these rectangles is 150 cm². If the length of rectangle ABCD is 27 cm and width is 20 cm, then what is the perimeter of rectangle PQRS?