Class 10 Mathematics Solutions English Medium

Quadratic Equations
Questions for practice

1 Marks questions;

Q1.   Write the discriminant of the quadratic equation 3x² - 5x - 11 = 0.

Q2.   For what value of k quadratic equation x² - kx + 4 = 0 has equal

         roots. 

Q3.   Write the nature of the roots of equation 4x² - 12x + 8 = 0. 

Q4.   What will be the value of D when given quadratic equation is a

         complete square. 

Q5.   Find the value of x in equation x² - 3 = 0.

Q6.   Write the value of x in equation x² - 15 = 0.   

Q7.   If x = - 2 is a root of the quadratic equation 3x² - 5x + 2k = 0. Then

         find the value of k. 

Q8.   For what value of k for which x = 3 is a solution of kx² - 2x - 1 = 0. 

Q9.   For what value of p the quadratic equation 2x² - 6x + p = 0 has

         real and distinct roots.  

Q10.  If one root of the equation x² + 7x + k = 0 is - 2, then find the value

          of k and other root. 

Q11.  For what value of k the given quadratic equation will be a

          complete square. 

Q12.  Find the solution of quadratic equation ax² – 2abx = 0. 

Q13.  Write a quadratic equation whose two roots are - 3 and 4. 

Q14.  Find the nature of equation (x – 2a ) (x – 2b ) = 4ab. 

Q15.  What is the middle term of a quadratic equation which roots are 

          - 4 and - 5 ?

Q16.  2 is the one of the root of quadratic equation 3x² - 11x + p = 0 then

          find the value of p. 

Q17.  Write the discriminant of the quadratic equation . 

Q18.  What is the nature of this equation. 

Q19.   For what value of k the equation x² + kx + 4 = 0 has no real roots?

Q20.   For what value of p the equation

           has real roots?

Q21.  Find the roots of given quadratic equation by the method of 

           completing the square. 

Q22.  Find the value of a nad b such that x = 1, x = - 2 are the solution

          of the quadratic equation x² + ax + b = 0.

Q23.   Solve for x

           abx² + (b² - ac) x - bc = 0

Q24.   solve for x

           3y² + (6 + 4a)y + 8a = 0

Q25.  Divide 51 in to two parts such that their product is 378.

Q26.  if the roots of the equation (b-c)x² + (c - a)x + (a - b) = 0 are equal

          then prove that 2b = a + c. 

Q27.  Find the value of k from the given equation so that equation 

          has equal roots. 

Q28.  Product of two number is 36 and difference is 9, find those number.

Q29.  Find the value of k if the equation has two equal and real roots.

Q30. Find the nature of following quadratic equations: 

(A)  x² + 4x + 9 = 0

(B)  3x² - 2x - 8 = 0

(C)  11x² + 8x - 3 = 0

(D)  x² + 7x + 4 = 0

(E)  x² + 4x + 4 = 0

(F)  3x² + 10x + 8 = 0

(G) 4x² + 3x + 5 = 0

(H)  7x² + 12x + 5 = 0

(I)  5x² - 10x + 5 = 0

Long-Answered Questions:

Q31. A journey of 192km from Mumbai to Pune takes 2hrs less by a fast train then by a slower train. If the speed of the slower train is 16 km/hr less than the faster train, find the speed of each train.

Q32. A part of monthly expenses of a family is constant and the remaining varies with the price of wheat. When the rate of wheat is Rs.250 per quintal, the total monthly expense if the family is Rs.1000 and when it is Rs.240 per quintal, the total monthly expense is Rs.980. Find the total monthly expenses of the family when cost wheat is Rs.350 per quintal.

Q33. A man travels 600km partly by train and partly by car. If he covers 400km by train and rest by car, it takes him 6hrs and 30minutes. But if he travels 200km by train and rest by car, he takes half an hour more. Find the speed of the train and that of the car.