Quadratic Equations Class 10 Extra Questions
MCQS (Quadratic Equations Class 10 Extra Questions)
- The quadratic equation ax2 + bx + c = 0 has two real and equal roots, then ‘c’ is equal to
a) –b/2a b) b/2a c) – b2/ 2a d) b2 / 4a - The quadratic equation x2 – 4x + k = 0 has distinct real roots if
a) k = 4 b) k > 4 c) k = 16 d) k < 4 - If ‘p’ is a root of the quadratic equation x2 – ( p + q)x + k = 0, then the value of ‘k’ is
a) p b) q c) p + 1 d) pq - The value(s) of k for which the quadratic equation 2x2 + kx +2 = 0 has equal roots, is
a) 4 b) +_ 4 c) – 4 d) 0 - The quadratic equation 2x2 – x + 1 =0 has
a) Two distinct real roots b) two equal real roots c) no real roots d) more than 2 real roots. - If y = 1 is a common root of the equations ay2 + ay +3 = 0 and y2 + y + b =0, then ab equals
a) 3 b) -7/2 c) 6 d) – 3 - The value of ….. is
a) 4 b) 3 c) – 2 d) 3.5 - If x2 + k ( 4x + k – 1) + 2 = 0 has equal roots, then k =
a) -2/3, 1               b) 2/3, 1                      c) 3/2, 1/3                   d) – 3/2, – 1/3
SUBJECTIVE TYPE QUESTIONS (Quadratic Equations Class 10 Extra Questions) - If 1+√2 is a root of a quadratic equation with rational coefficients, write its other root.
- Write a quadratic equation sum of whose roots is 2 and their product is 2.
- If the equation x2 + 4x + k = 0 has real and distinct roots, then find the value of k.
- If the equation x2 -bx + 1 = 0 does not possess real roots, then find the value of b.
- Check whether (x – 4)3 + 20 = x3 + 2x is quadratic or not.
- Write the discriminant of the quadratic equation (x + 5)2 =2(5x-3).
- If a and b are roots of the equation x2 +ax +b=0 then find the value of a+b.
- If the quadratic equation has two equal roots, then find the value of p.
- For what value of ‘a’ quadratic equation 4x2 – 12x – a = 0 has no real roots?
- Which are two consecutive odd positive integers, sum of whose squares is 290?
- If the difference of roots of the quadratic equation x2 + kx + 12 = 0 is 1, then what is positive value of k.
20. Find positive value(s) of k for which both quadratic equations x2 + kx + 64 = 0 and x2 – 8 x + k = 0 will have real roots.
21. Find the discriminant and hence nature of roots of 2x2 – 4x + 3=0.
22. Find the value of ‘k’ for which following quadratic equation have equal roots: kx (x-2) + 6 = 0
23. If x2 + 2kx + 4 = 0 has a root x = 2, then find the value of k .
24. If the quadratic equation px2 – 2√5px + 15 = 0 has two equal roots, then find the value of p
25. Solve for x :
(a) p2x2 + (p2 – q2) x – q2 = 0 (b) 36 x2 – 12ax + a2 – b2 = 0 c) 4x2 + 4bx – (a2 – b2 ) = 0
26. Find the value of k for which the given equation x2 – 4 x + k = 0 has distinct real roots
27. If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p( x2 + x ) + k = 0 has equal roots. Find the value of k.
28. If x = -2 is a root of the equation 3x2 + 7x + p = 0, find the values of k so that the roots of the equation    x2 + k(4x + k – 1) + p = 0 are equal.
29. The area of a right-angled triangle is 600 sq cm. If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.
30. The hypotenuse (in cm) of a right angled triangle is 6 cm more than twice the length of the shortest side. If the length of the third side is 6 cm less than thrice of the length of shortest side, the find the dimensions of the triangle.
31. A peacock is sitting on the top of a pillar, which is 9m high. From a point 27m away from the bottom of a pillar seeing the snake, the peacock pounces on it. If their speeds are equal, at what distance from the hole is the snake caught ?
32. In a fight of 600 km, an aircraft was was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr from its usual speed and the time of the flight increased by 30 mins . Find the scheduled duration of the flight.
33. A shopkeeper buys some books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost Re 1 less. Find the number of books he bought.
34. At present Aasha’s age (in yrs) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age , Aasha’s age would be 1 year less than 10 times the present age of Nisha. Find the present age of Aasha and Nisha.
35. Assertion: If one root of the quadratic equation 6x2 – x – k = 0 is 2/3, then value of k is 2.
Reason: The quadratic equation ax2 + bx + c = 0, a ≠0 has almost two roots.
36. Assertion: (2x – 1)2 – 4x2 + 5 = 0 is not a quadratic equation.
Reason: An equation of the form ax2 + bx + c = 0, a ≠0, where a, b, c ∈ R is called a quadratic
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Quadratic Equations Class 10 Extra Questions
Quadratic Equations Class 10 Extra Questions
Quadratic Equations Class 10 Extra Questions
Quadratic Equations Class 10 Extra Questions
Quadratic Equations Class 10 Extra Questions
