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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?
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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.
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.
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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?
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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?.
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?.
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