CAT Exam  >  CAT Questions  >  If a quadratic equation x2−ax+bhas root... Start Learning for Free
If a quadratic equation x2−ax+b has roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q​, where p and q are co-prime natural numbers. Then the value of p-q=?
    Correct answer is '21'. Can you explain this answer?
    Verified Answer
    If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then ...
    Let the roots of the given equation be k and 4k.
    Then sum of roots= 5k = - (-α−1)​ = α
    And product of roots= 4k2 =  b/1​ or b.
    So, a = 5k and b = 4k2.
    So, b-4a+3= 4k2−4(5k)+3 = 4k2−20k+3.
    So, the given expression reduces to the form of a quadratic expression, which opens upward (Co-efficient of k2 is 1, which is positive)
    For any quadratic equation of the form αx2+bx+c, the minima occurs at -b/α​ and the minima= - D/4α​, where D is the discriminant of the quadratic equation.
    In our case, 4k2−20k+3 has a= 4, b = -20 and c=3.
    D= b2−4ac = (-20)2 −4×4 ×3 = 400−48 = 352
    4a  = 16.
    .'. Minima= - D/4α ​= − 352/16 = −22 or −22/1​.
    So, p = 22, q = 1. .'. p-q= 22-1 = 21.
    View all questions of this test
    Most Upvoted Answer
    If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then ...
    If a quadratic equation x^2 + bx + c = 0 has two equal roots, then the discriminant, b^2 - 4ac, is equal to zero.
    Attention CAT Students!
    To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
    Explore Courses for CAT exam

    Similar CAT Doubts

    If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer?
    Question Description
    If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer?.
    Solutions for If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
    Here you can find the meaning of If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer?, a detailed solution for If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer? has been provided alongside types of If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If a quadratic equation x2−ax+bhas roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q, where p and q are co-prime natural numbers. Then the value of p-q=?Correct answer is '21'. Can you explain this answer? tests, examples and also practice CAT tests.
    Explore Courses for CAT exam

    Top Courses for CAT

    Explore Courses
    Signup for Free!
    Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
    10M+ students study on EduRev