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Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?
- a)15
- b)14
- c)24
- d)26
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Find the value of a/b + b/a, if a and b are the roots of the quadratic...
a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab
= [(a + b)2 - 2ab]/ab
a + b = -8/1 = -8
ab = 4/1 = 4
Hence a/b + b/a = [(-8)2 - 2(4)]/4 = 56/4 = 14.
Most Upvoted Answer
Find the value of a/b + b/a, if a and b are the roots of the quadratic...
Finding the value of a/b and b/a for the given quadratic equation.
Given quadratic equation is x^2+8x+4=0. Let the roots of the equation be a and b.
Sum of roots, a+b=-8 and product of roots, ab=4.
Therefore, a/b and b/a can be written as (a/b)+(b/a) and (a/b)(b/a) respectively.
Using the identity (a+b)^2=a^2+b^2+2ab, we get:
(a+b)^2=a^2+b^2+2ab
(-8)^2=a^2+b^2+2(4)
64=a^2+b^2+8
a^2+b^2=56
Now, (a/b)+(b/a) can be obtained by multiplying and dividing (a/b)+(b/a) by (a*b), we get:
(a/b)+(b/a)=(a^2+b^2)/(ab)
(a/b)+(b/a)=(56/4)
(a/b)+(b/a)=14
Similarly, (a/b)(b/a) can be obtained as:
(a/b)(b/a)=(ab)/(ab)
(a/b)(b/a)=1
Therefore, the value of (a/b)+(b/a) is 14 and the value of (a/b)(b/a) is 1.
Hence, the correct answer is option B) 14.
Given quadratic equation is x^2+8x+4=0. Let the roots of the equation be a and b.
Sum of roots, a+b=-8 and product of roots, ab=4.
Therefore, a/b and b/a can be written as (a/b)+(b/a) and (a/b)(b/a) respectively.
Using the identity (a+b)^2=a^2+b^2+2ab, we get:
(a+b)^2=a^2+b^2+2ab
(-8)^2=a^2+b^2+2(4)
64=a^2+b^2+8
a^2+b^2=56
Now, (a/b)+(b/a) can be obtained by multiplying and dividing (a/b)+(b/a) by (a*b), we get:
(a/b)+(b/a)=(a^2+b^2)/(ab)
(a/b)+(b/a)=(56/4)
(a/b)+(b/a)=14
Similarly, (a/b)(b/a) can be obtained as:
(a/b)(b/a)=(ab)/(ab)
(a/b)(b/a)=1
Therefore, the value of (a/b)+(b/a) is 14 and the value of (a/b)(b/a) is 1.
Hence, the correct answer is option B) 14.
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Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2+ 8x + 4 = 0?a)15b)14c)24d)26e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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