NCERT Class 10 Mathematics Quadratic Formative Assessment CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2023)
Glide to success with Doorsteptutor material for CBSE/Class-10 : get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-10.
Quadratic Formative assessment
Question 1. State which all quadratic equations have real roots, no real roots
a)
b)
c)
d)
e)
f)
g)
h)
Solution
Nature of roots of Quadratic equation
S. no | Condition | Nature of roots |
1 | Two distinct real roots | |
2 | One real root | |
3 | No real roots |
Real roots: (b) , (d) , (e) , (f) , (g)
No real roots: (a) , (c) , (h)
Question 2. Find the roots of the quadratic equation using factorization technique
a)
b)
Solution
So roots are and 5
b) Roots are 5 and 6
Question 3. Find the roots of the quadratic equation using square method
a)
b)
Solution
b)
or
Question 4 -True or False statement
a) There are no reals roots of the quadratic equation
Solution: True
b) The roots of the equation are
Solution: True
c) A quadratic equation can have at most 2 real roots
Solution: True
d) In a quadratic equation , if a and c are of same sign and b is zero, the quadratic equation has real roots
Solution: False
e) In a quadratic equation , if a and c are of opposite sign, then quadratic equation will definitely have real roots
Solution: True
f) For , the quadratic equation will definitely have real roots
Solution: True
g) If the roots of the quadratic equation are rational, the coefficient of the term x will also be rational.
Solution: True
h) If the roots of the quadratic equation are irrational, the coefficient of the term x will also be irrational
Solution: True
I) Every quadratic equation will have rational roots
Solution: False
Multiple-choice Questions
Question 7 Find a natural number whose square diminished by 84 is thrice the 8 more of given number
a) 21
b) 13
c) 11
d) 12
Solution (d)
So answer is 12
Question 8. The roots of the quadratic equation
are
a)
b)
c)
d)
Solution (c)
Question 9. The equation
a) Is a quadratic equation
b) Is not a quadratic equation
Solution b
Question 10. The roots of the quadratic equation
a) Are real
b) Are not real
Solution (b)