MULTIPLE CHOICE QUESTIONS: (MCQ’s)
1.Which of the following is not a quadratic equation.
(a) x² + 3x – 5 = 0
(b) x² + 4x³ + 2 = 0
(c) 3 + x + x² = 0
(d) x² – 9 = 0
2. A quadratic equation has degree_____
(a) 0
(b) 1
(c) 2
(d) 3
3. The equation (x² + 1)² – x² = 0 has______
(a) Four real roots
(b) Two real roots
(c) No real roots
(d) One real roots
4. The polynomial equation x (x + 1) + 8 = (x + 2) (x – 2) is:
(a) Linear equation
(b) Quadratic equation
(c) Cubic equation
(d) Bi-quadratic equation
5. If −5 is a root of the quadratic equation 2x² + px – 15 = 0, then:
(a) p = 3
(b) p = 5
(c) p = 7
(d) p = 1
6. Karen solves an equation. After solving she finds the roots as 8 and 2.
The equation she solved was:
(a) x² −10x + 16
(b) x² +10x + 16
(c) x² −10x + 7
(d) 2x² −10x + 16
7. If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, the value of k is:
(a) 1
(b) −1
(c) −2
(d) 2
8. The sum of the roots of the quadratic equation 3x² – 9x + 5 = 0 is:
(a) 3
(b) 6
(c) −3
(d) 2
9. The quadratic equation whose roots are 6 , 1 is:
(a) x² – 7x + 5 = 0
(b) x² + 7x + 6 = 0
(c) x² – 7x + 6 = 0
(d) x² – 6x + 7 = 0
10. The quadratic equation whose roots are −6,−1 is:
(a) x² – 7x + 5 = 0
(b) x² + 7x + 6 = 0
(c) x² – 7x + 6 = 0
(d) x² – 6x + 7 = 0
11 Which are the following are quadratic equations
(i) x² – 6x + 4 = 0 (ii) 2x² – 6x + 7 = 0
(a) None
(b) Only (i)
(c) Both (i) and (ii)
(d) Only (ii)
12.Which of the following is a solution of the quadratic equation
(i) 3x2 –x = 0 for x =1 (ii) 6x² −5x = 0 for x = −1
(a) none
(b) only (i)
(c) both (i) and (ii)
(d) only (ii)
13. The product of two consecutive positive integers is 24 so the equation will be_____
(a) x2 + x + 24 = 0
(b) x2 + x −24 = 0
(c) x2 + 2x − 24 = 0
(d) x2 + 2x + 24 = 0
14. The roots of x2 −5x + 6 = 0 will be _______
(a)−2,−5
(b) 2, 3
(c)−2,−3
(d) −2,3
15. The zeros of (x−4) (x + 2) = 0 are ____
(a) 4,−2
(b) 4,2
(c)−4, 2
(d)−4,−2
16. The given equation is 9x2 + 7x −2 = 0 ... the value of discriminant (D) = ____
(a) 121
(b) 120
(c) 141
(d) 131
17. If D = b2 − 4ac > 0 then the roots are ____
(a) Unique
(b) Real
(c) Do not exist
(d) Equal
18. If D = b2 −4ac = 0 then the roots are _____
(a) Do not exist
(b) Real,not equal
(c) Unique
(d) Real, equal
19. The nature of roots of the quadratic equation 3x2 −4√3x + 4 = 0 are _____
(a) Real ,unequal
(b) Unique
(c) Real, equal
(d) Do not exist
20.The sum of the squares of two consecutive numbers is 30.
The equation will be _____
(a) 2x2 + 2x − 29 = 0
(b) 3x2 − 2x + 30 = 0
(c) 3x2 + 2x − 20 = 0
(c) 2x2 −2x + 29 = 0
21.The sum of a number and its reciprocal is 20.
The equation will be _____
(a) x2−10x + 1 = 0
(b) x2+20x − 1= 0
(c) 2x2 −20x + 1 = 0
(d) x2 −20x + 1 = 0
22. The two digit number whose digits in the tens and units place
be ‘x’ and ‘y’ respectively then the number will be _____
(a) 10x + y
(b) 10x −y
(c) 10y + x
(d) 10y −x
23. If the equation x2 −ax + 1 = 0 has two distinct roots then _____
(a) a = 2
(b) a < 2
(c) a > 2
(d) None of these
24. If the equation 9x² + 6kx + 4 = 0 has equal roots, then
the roots are both equal to ____
(a) ± 2/3
(b) ± 3/2
(c) 0
(d) ± 3
25. If ax²+ bx + c = 0 has equal roots, then c = _____
(a) −b/2a
(b) b/2a
(c) –b²/4a
(d) b²/4a
26. The discriminant of the equation 3x² −2x+ 1/3 is ____
(a) 2
(b) 4
(c) 0
(d) 1
27. The discriminant of the quadratic equation 2x² −4x + 3 = 0 is −8 .
So the nature of roots will be ______
(a) No real roots
(b) Real roots
(c) Equal roots
(d) Roots do not exist
28. The roots of the equation 2x² −5x + 3 = 0 is ____
(a) 4 , 3/2
(b) 2 , 3/4
(c) 3/3 , 2
(d) 3/2 , 1
29. Which of the following equations has 2 as a root?
(a) x² – 4x + 5 = 0
(b) x² + 3x – 12 = 0
(c) 2x² – 7x + 6 = 0
(d) 3x² – 6x – 2 = 0
30. Which of the following has the sum of its roots as 3?
(а) 2x² – 3x + 6 = 0
(b) -x² + 3x + 3 = 0
(c) √2x² – 3√2x + 1 = 0
(d) 3x² – 3x + 3 = 0
31. The sum and the product of the zeroes of a quadratic equation in x are 3 and 0 .
Then the polynomial is ______
(a) 2x² − 3x
(b) 3x² − 3x
(c) x² − 3x
(d) x² − 9x
32. If α and β are the zeroes of a quadratic equation 2x² − 5x − 7 then α + β = _____
(a) 5/2
(b) 4/7
(c) 2/7
(d) 5/7
33. Find the sum of the zeroes of the quadratic equation 2x² − 7x −15
(a) 5/2
(b) 4/7
(c) 2/7
(d) 7/2
34. Find the zeroes of the quadratic equation x² − 7x
(a) 0 ,3
(b) 0 , 7
(c) 2 , 7
(d) 3 , 5
35. Find the zeroes of the quadratic equation x² − 13x + 36
(a) 6 , 9
(b) 5 , 7
(c) 4 , 7
(d) 4 , 9
Answers + Clues:
1 (b) ⇒ The quadratic equation should be of the form ax² + bx + c =0
2 (c) ⇒ The highest power in a quadratic equation is 2
3 (c) ⇒ Open the brackets solve it full and then conclude
4 (a) ⇒ Solving it we get (x + 12)
5 (c) ⇒ Put x = −5 and get value of p
6 (a) ⇒ The factors are (x−8) (x−2).Then solve it
7 (b) ⇒ Put x = 2 and solve for k
8 (c) ⇒ Sum of roots = −b/a
9 (c) ⇒ The factors are (x−6) (x−1). Then solve it
10 (b) ⇒The factors are (x +6) (x+1). Then solve it
11 (c)⇒ Definition of Quadratic Equation
12 (a) ⇒ Put the given values and check
13 (b) ⇒ Make the equation from the given sum
14 (b) ⇒ Solve the two equations
15 (a) ⇒ Solve and find the zeroes
16 (a) ⇒ Put D = b² − 4ac and find it
17 (b) ⇒ Textbook
18 (d) ⇒Textbook
19 (c) ⇒ Find b² −4ac and then say what kind of roots
20 (a) ⇒ Make the equation from the given statement
21 (d) ⇒ Number is x and the reciprocal is 1/x. Add both and equate it to 20 and solve
22 (a) ⇒ General form of two digit number
23 (c) ⇒ Summary
24 (a) ⇒ Summary
25 (d) ⇒ If equal roots then b² −4ac = 0 and find value of c
26 (c) ⇒ Find the value of b² −4ac
27 (a) ⇒ (Example 16) Textbook
28 (d) ⇒ (Example 3) Textbook
29 (c) ⇒ Factorise and find the roots
30 (b) ⇒ Put sum of roots formula
31 (c) ⇒ Put x² + ( α + β) + αβ formula
32 (a) ⇒ Find out the two roots and add them
33 (d) ⇒ Find out the two roots and add them
34 (b) ⇒ Factorise and find the roots
35 (d) ⇒ Factorise and find the roots