Latest SELF Aptitude Question SOLUTION: If roots of equation x^2+px+q=0 are tan30 and tan15. then determine value of 2+q-p. A)0 B)1 C)2 D)3

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If roots of equation x^2+px+q=0 are tan30 and tan15. then determine value of 2+q-p.
A)0
B)1
C)2
D)3

harshal agrawal (10 years ago)

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ANUP KUMAR  (10 years ago)

tan30 and tan15 are roots of equation x^2+px+q=0

then, tan30+ tan15= -p
and tan30 * tan15= q

HERE,
tan45= tan(30+15)
tan45= (tan30+tan15)/(1-tan30 * tan15)
1 = -p/(1-q)
1-q= -p
1=q-p
ADDING 2 BOTH SIDES THEN,
2+1 = 2+q-p
2+q-p = 3 ans

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RAKESH  (10 years ago)

D) 3

x^2+px+q=0, roots are tan30 & tan15

sum of roots = tan30 + tan15 = -p

product of roots = tan30 * tan15 = q

2+q-p
= 2 + tan30 * tan15 + tan30 + tan15
= 2 +( tan15 + tan30 + tan15*tan30 )
= 2 + 1
= 3
-------------
tan(30+15)= tan45 = (tan30 + tan15)/(1- tan30*tan15)
=> 1- tan30*tan15 = tan30 + tan15
=> tan15 + tan30 + tan15 * tan30 = 1

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Ann Theressa  (10 years ago)

3

A quadratic equation is of the form,
x^2 - (sum of roots)x + (product of roots) = 0

Here,
Sum of roots = -p
product of roots = q

ie,
tan 30 + tan 15 = -p
tan 30*tan 15 = q

2+q-p = 2+tan 30*tan 15 + tan 30 + tan 15
=1 + (1+tan 15)(1+tan 30)
= 1 + 2
=3

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