/20 1234567891011121314151617181920 Test Code: MC4L3 1 / 20 1. Which of the following is a quadratic equation? A) x³ – x² =(x -1)³ B) (k + 1)x² + – x = 7, where k = -1 C) x² + 2x + 1 = (4 – x)² + 3 D) -2x² = (5 – x) (2x – 2/5) 📝 Solution: 2 / 20 2. Every quadratic equation has atmost two roots. A) False B) True 📝 Solution: True, because every quadratic polynomial has atmost two roots. 3 / 20 3. If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots. A) False B) True 📝 Solution: True, since in this case discriminant is always positive, so it has always real roots, e., ac < 0 and so, b2 – 4ac > 0. 4 / 20 4. A quadratic equation with integral coefficient has integral roots. Justify your answer. A) Yes B) No C) I don't know 📝 Solution: No, consider the quadratic equation 2x² + x – 6=0 with integral coefficient. The roots of the given quadratic equation are -2 and which are not integers. 5 / 20 5. If the coefficient of x² and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots. A) False B) True 📝 Solution: True, since in this case discriminant is always negative, so it has no real roots e., if b = 0, then b2 – 4ac ⇒ – 4ac < 0and ac>0. 6 / 20 6. Which of the following is not a quadratic equation? A) 2 (x -1)² = 4x² – 2x +1 B) (x² + 2x)² = x⁴ + 3 + 4x² C) (-√2X +√3)² = 3x² – 5x D) 2x – x² = x² + 5 📝 Solution: 7 / 20 7. Every quadratic equation has atleast two roots. A) False B) True 📝 Solution: False, since a quadratic equation has two and only two roots. 8 / 20 8. Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer. A) I don't know B) No C) Yes 📝 Solution: Yes, consider the quadratic equation 2x² + x – 4 = 0 with rational coefficient. The roots ofthe given quadratic equation are -1 + √33/4 and -1 – √33/4 are irrational. 9 / 20 9. Value(s) of k for which the quadratic equation 2x² -kx + k = 0 has equal roots is/are A) 8 B) 0, 8 C) 4 D) 0 📝 Solution: 10 / 20 10. Which of the following equations has the sum of its roots as 3? A) √2x² – x + 1 = 0 B) -x² + 3x – 3 = 0 C) 2x² – 3x + 6 = 0 D) 3x² – 3x + 3 = 0 📝 Solution: 11 / 20 11. (x² +1)² – x² = 0 has A) four real roots B) two real roots C) no real roots D) one real root 📝 Solution: 12 / 20 12. If is a root of the equation x² + kx – = 0, then the value of k is: A) 1/2 B) 1/4 C) 2 D) -2 📝 Solution: 13 / 20 13. Which of the following equations has two distinct real roots? A) x² + x – 5 =0 B) 2x² – 3√2x + 9/4 =0 C) 5x² – 3x + 1=0 D) x² + 3x + 2√2 =0 📝 Solution: 14 / 20 14. Does there exist a quadratic equation whose coefficient are all distinct irrationals but both the roots are rationals? why? A) I don't know B) No C) Yes 📝 Solution: Yes, consider the quadratic equation with all distinct irrationals coefficients i.e., √3x² – 7 √3x + 12√3 = 0. The roots of this quadratic equation are 3 and 4, which are rationals. 15 / 20 15. Every quadratic equation has exactly one root. A) False B) True 📝 Solution: False, since a quadratic equation has two and only two roots. 16 / 20 16. 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 📝 Solution: 17 / 20 17. Which of the following equations has no real roots? A) x² – 4x – 3√2 = 0 B) x² + 4x – 3√2=0 C) x² – 4x + 3√2 =0 D) 3x² + 4√3x + 4=0 📝 Solution: 18 / 20 18. The quadratic equation 2x² – √5x + 1 = 0 has A) two equal real roots B) two distinct real roots C) more than 2 real roots D) no real roots 📝 Solution: 19 / 20 19. Which constant must be added and subtracted to solve the quadratic equation 9×2 + x – √2= 0 by the method of completing the square? A) 9/64 B) 1/8 C) 1/4 D) 1/64 📝 Solution: 20 / 20 20. Every quadratic equation has atleast one real root. A) False B) True 📝 Solution: False, for example x2 + 4 = O has no real root. Your score isShare Your Score with Friends Facebook Twitter 0% Send feedback
