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If α, β are the roots of the quadratic equation ax2 + bx + c = 0 and 3b2 = 16ac then
  • a)
    α = 4β or β = 4α
  • b)
    α = –4β or β = –4α
  • c)
    α = 3β or β = 3α
  • d)
    α = –3β or β = –3α
Correct answer is option 'C'. Can you explain this answer?
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If α, β are the roots of the quadratic equation ax2 + bx + ...
3b2 = 16ac
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Most Upvoted Answer
If α, β are the roots of the quadratic equation ax2 + bx + ...
Alpha * beeta = c/a equation (l)
alpha + beeta = -b/a equation (1)
doing square both sides before multiplying by (3a^2) both sides in equation (1) :-
3a^2(alpha + beta )^2 = 3 b^2
so,
3a^2(alpha square + beeta square + 2alpha beeta) = 16ac
or,
(alpha square + beeta square + 2c/a ) = (16/3)c/a
alpha square + beeta square = ( 16c/3a ) - (2c/a)
alpha square + beeta square = (16c - 6c)/3a
alpha square + beeta square = (10/3)(alpha * beeta) (using equation (l))
so,
3alpha square + 3 beeta square - 2 x 5 alpha * beeta = 0
let :- alpha = t , beeta = b
3t^2 - 10tb + 3b^2 = 0
t = (10b + √(100b^2 - 36b^2))/6
or,
t = ( 10b + 8b) /6
= 18b/6. = 3b
again similarly,
t = (10b - 8b)/6 = b/3
so,
3t = b
hence:-
alpha = 3 beeta
and 3alpha = beeta
thus we can say that the option (c) is the correct option
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If α, β are the roots of the quadratic equation ax2 + bx + ...
3b2 = 16ac
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If α, β are the roots of the quadratic equation ax2 + bx + c = 0 and 3b2 = 16ac thena)α = 4β or β = 4αb)α = –4β or β = –4αc)α = 3β or β = 3αd)α = –3β or β = –3αCorrect answer is option 'C'. Can you explain this answer?
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If α, β are the roots of the quadratic equation ax2 + bx + c = 0 and 3b2 = 16ac thena)α = 4β or β = 4αb)α = –4β or β = –4αc)α = 3β or β = 3αd)α = –3β or β = –3αCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If α, β are the roots of the quadratic equation ax2 + bx + c = 0 and 3b2 = 16ac thena)α = 4β or β = 4αb)α = –4β or β = –4αc)α = 3β or β = 3αd)α = –3β or β = –3αCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α, β are the roots of the quadratic equation ax2 + bx + c = 0 and 3b2 = 16ac thena)α = 4β or β = 4αb)α = –4β or β = –4αc)α = 3β or β = 3αd)α = –3β or β = –3αCorrect answer is option 'C'. Can you explain this answer?.
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