Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Quadratic Equation and Inequalities question

2005 · Shift 0 · Q68
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Mathematics
  4. /Quadratic Equation and Inequalities
  5. /2005 · Shift 0 · Q68

Quadratic Equation and Inequalities question

2005 · Shift 0 · Q68

JEE MainMathematicsQuadratic Equation and InequalitiesMCQ+4 / −1
If the roots of the equation x2−bx+c=0{x^2} - bx + c = 0x2−bx+c=0 be two consecutive integers, then b2−4c{b^2} - 4cb2−4c equals
  1. A
    −2-2−2
  2. B
    333
  3. C
    222
  4. D
    111
View written solutionFree

Correct answer: D

  1. Let the two consecutive integer roots be nnn and n+1n+1n+1, where nnn is an integer.

  2. For the quadratic equation x2−bx+c=0,x^2-bx+c=0,x2−bx+c=0, by Vieta’s formulas:

    • Sum of roots =b= b=b
    • Product of roots =c= c=c

  3. Using the roots nnn and n+1n+1n+1: b=n+(n+1)=2n+1b=n+(n+1)=2n+1b=n+(n+1)=2n+1 c=n(n+1)=n2+nc=n(n+1)=n^2+nc=n(n+1)=n2+n

  4. Now compute: b2−4c=(2n+1)2−4(n2+n)b^2-4c=(2n+1)^2-4(n^2+n)b2−4c=(2n+1)2−4(n2+n)

  5. Expanding: b2−4c=4n2+4n+1−4n2−4n=1b^2-4c=4n^2+4n+1-4n^2-4n=1b2−4c=4n2+4n+1−4n2−4n=1

  6. Therefore, b2−4c=1b^2-4c=1b2−4c=1

  7. Checking options:

    • A: −2-2−2 ❌
    • B: 333 ❌
    • C: 222 ❌
    • D: 111 ✅

Hence, the correct answer is D.

PreviousNext

More from Quadratic Equation and Inequalities

  • The value of a for which the sum of the squares of the roots of the equation x2−(a−2)x−a−1=0 assume the least value is :2005 · MCQ
  • In a triangle PQR,∠R=2π​.Iftan(2P​) and tan(2Q​) are the roots of ax2+bx+c=0,ae0 then2005 · MCQ
  • If both the roots of the quadratic equation x2−2kx+k2+k−5=0 are less than 5, then k lies in the interval2005 · MCQ
  • Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation2004 · MCQ
  • If (1−p) is a root of quadratic equation x2+px+(1−p)=0 then its root are2004 · MCQ
  • If one root of the equation x2+px+12=0 is 4, while the equation x2+px+q=0 has equal roots, then the value of ′q′ is2004 · MCQ
  • If the sum of the roots of the quadratic equation ax2+bx+c=0 is equal to the sum of the squares of their reciprocals, then ca​,ab​ and bc​ are in2003 · MCQ
  • The value of 'a' for which one root of the quadratic equation (a2−5a+3)x2+(3a−1)x+2=0 is twice as large as the other is2003 · MCQ