Quadratic Equation

Hello guys,
Let's start our mcq series with video solution

1. What are the roots of the equation log10(x²-6x+45)=2?

(A) 9,-5
(B) -9,5
(C) 11,-5
(D) -11,5

【video solution】

2. For what value of k, will roots of the equation kx²-5x+6=0 be in the ratio of 2:3?

(A) 0

(B) 1

(C) -1

(D) 2


3. What is the solution of the equation [x/(x+3)]½-[(x+3)/x]½=-3/2?

(A) 1

(B) 2

(C) 4

(D) None of these


4. If the equation 2x²-7x+12=0 has two roots A and B, then the value of A/B+B/A is -

(A) 7/2

(B) 1/24

(C) 7/24

(D) 97/24


5. If 2(x²+1/x²)-(x-1/x)-7=0 then two values of x are:

(A) 1,2

(B) 2,-1/2

(C) 0,1

(D) 1/2,1


6. If m and n are the roots of the equation ax²+bx+c=0, then the equation whose roots are (m²+1)/m and (n²+1)/n is :

(A) acx²+(ab+bc)x+b²+(a-c)²=0

(B) acx²+(ab-bc)x+b²+(a-c)²=0

(C) acx²+(ab-bc)x+b²-(a-c)²=0

(D) acx²+(ab+bc)x+b²-(a-c)²=0


7. In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtain 8 and 2 for the roots. The correct equation was

(A) x²+10x+9=0

(B) x²-10x+16=0

(C) x²-10x+9=0

(D) none of these


8. If m and n (m>n) are the roots of the equation 7(x+2a)²+3a²=5a(7x+23a), where a>0, then what is 3m-n equal to?

(A) 12a

(B) 14a

(C) 15a

(D) 18a


9. If 5x+9y=5 and 125x³+720y³=120 then the value of the product of x and y is:

(A) 1/9

(B) 1/135

(C) 45

(D) 135


10. If the roots of the equation lx²+me+m=0 are the ratio p:q, then √(p/q) +√(q/l) + √(m/l) is equal to 

(A) 0

(B) 1

(C) 2

(D) 3


11. If √(3x²-7x-30)-√(2x²-7x-5)=x-5 has a and b as its roots, then the value of ab is :

(A) -15

(B) -5

(C) 0

(D) 5


12. What are the roots of the equation 2^(x+2).27^(x/x-1)=9?

(A) 2, 1-log(3/2)

(B) 2, 1-log(2/3)

(C) -2, 1-(log3/log2)

(D) -2, 1-(log2/log3)


13. If ∆ is an integer and a,b are the roots of 4x²-16x+∆/4=0 such that 1<a<2 and 2<b<3, then how many values can l take?

(A) 3

(B) 9

(C) 14

(D) 15


14. If the some of the roots of a quadratic equations is 1 and product of the roots is -20. Find the quadratic equation.

(A) x²-x-20=0

(B) x²-x+20=0

(C) x²+x-20=9

(D) None of these


15. If a and b are the roots of equation x²-x+1=0, then which equation will have roots a³ and b³?

(A) x²+2x+1=0

(B) x²-2x-1=0

(C) x²+3x-1=0

(D) x²-3x+1=0


16. A root of equation ax²+bx+c=0 (where a, b and c are rational numbers) is 5+3√3. What is the value of (a²+b²+c²)/(a+b+c)?

(A) 35/3

(B) 37/3

(C) -105/11

(D) -105/13


17. If a and b are the roots of the equation x²+x-1=0, then what is the equation whose roots are a⁵ and b⁵?

(A) x²+7x-1=0

(B) x²-7x-1=0

(C) x²-11x-1=0

(D) x²+11x-1=0


18. If the roots of the equation a(b-c)x²+b(c-a)x+c(a-b)=0 are equal, then which of following is true?

(A) b=(a+c)/ac

(B) 2/b=(1/a)+(1/c)

(C) 2b=(1/a)+(1/c)

(D) abc=ab+bc+ca


19. If a and b are the roots of equation x²-2x+4=0, then what is the equation whose roots are a³/b² and b³/a²?

(A) x²-4x+8=0

(B) x²-32x+4=0

(C) x²-2x+4=0

(D) x²-16x+4=0


20. If one root of the equation Ax²+Bx+C=0 is two and a half times the others, then which of the following is TRUE?

(A) 7B²=3CA

(B) 7B²=4CA

(C) 7B²=36CA

(D) 10B²=49CA


21. If the difference between the roots of the equation Ax²-Bx+C=0 is 4, then which of the following is TRUE?

(A) B²-16A²=4AC+4B²

(B) B²-10A²=4AC+6A²

(C) B²-8A²=4AC+10A²

(D) B²-16A²=4AC+8B²


22. A and B are the roots of quadratic equation. If A+B =8 and A-B=2√5, then which of the following equation will have roots A⁴ and B⁴?

(A) x²-1522+14641=0

(B) x²+1921x+14641=0

(C) x²-1764x+14641=9

(D) x²+2520x+14641=0


23. If a and b are the roots of the equation PX²-QX+R=0 then what is the value of (1/a²)+(1/b²)+(a/b)+(b/a)?

(A) (Q²-2p)(2R+P)/PR²

(B) (Q²-2PR)(R+P)/PR²

(C) (Q²-2R)(2P+R)/P²R²

(D) (Q²-2PR)(2R+2P)/P²R²


24. If A and B are the roots of the equation Ax²-A²x+AB=0, then what is the value of A and B respectively ?

(A) 1,0

(B) 1,1

(C) 0,2

(D) 0,1


25. Alpha and beta are the roots of the quadratic equation x²-x-1=0. What is the value of alpha⁸+b⁸?

(A) 47

(B) 54

(C) 59

(D) 68


26. If a and b are roots of the equation ax²+bx+c=0, then which equation will have roots (ab+a+b) and (ab-a-b)?

(A) a²x²+2acx+c²+b²=0

(B) a²x²-2acx+c²-b²=0

(C) a²x²-2acx+c²+b²=0

(D) a²x²+2acx+c²-b²=0


27. If A and B are the roots of equation x²+Ax+B=0 then find A³+B³

(A) -7

(B) 8

(C) -8

(D) 7


28. Which of the following equations has 3 as a root?

(A) x²-7x+12=0

(B) x²-5x+12=0

(C) x²+3x+12=0

(D) x²+3x-12=0


29. Which of the following equations has the sum of its roots as 5?

(A) x²-5x+6=0

(B) x²+5x-6=0

(C) x²+5x+6=0

(D) None of these


30. What are the roots of the quadratic equation: x²+3x-154=0?

(A) 11,14

(B) 11,-14

(C) 14,-11

(D) 14,-22

 

31. Which of the following quadratic equations has real roots?

(A) 4x²-3x+6=0

(B) 2x²+7x+6=0

(C) x²-2x+4=0

(D) 3x²-4x+3=0


32. Which of the following quadratic equations has equal roots?

(A) x²-14x-49=0

(B) x²+7x+49=0

(C) x²-7x-49=0

(D) x²+14x+49=0


33. Factorise x²+5x-14

(A) (x-7)(x+2)

(B) (x-1)(x+14)

(C) (x+7)(x-2)

(D) (x-14)(x+1)


34. If x²+1/x²=11, then x-1/x is equal to :-

(A) 2

(B) 3

(C) 5

(D) 4


35. If x+1/x = 4√3, then x²+1/x² is equal to :-

(A) 46

(B) 44

(C) 56

(D) 52


36. If x+1/x = 8 then the value of x²+1/x² is :

(A) 68

(B) 62

(C) 66

(D) 64