Quadratic equation

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Q1. x2 + ax + b = 0 and x2 + bx + a =0 have a common root, then which of the following is true?
a. a + b =0
b. a + b = 1
c. a + b = -1
d. a + 2b = -3

Q2. If one root of the equation ax2 + bx + c = 0 is 3 times other root, then which of the following is true?
a. 3b2 = ac
b. 3b3 = 28ac
c. b2 = 16ac
d. 3b2 = 16ac

Q3. The arithmetic mean of the squares of the reciprocals of the roots of the equation
(√3 –1 )x2  - (2 + √3)x + (√3 + 1) = 0 is
a. (-6 – 5 √3)/4
b. (6 + 5 √3)/4
c. (6 – 5 √3)/4
d. (-6 + 5 √3)/4

Q4. Let p and q be the roots of the equation x2 – 2x + A = 0 and let r and s be the roots of the equation x^2 – 18x + B =0 .
If p < q < r < s are in the arithmetic progression, then A, B respectively equal to
a. 8, 17
b. 3, 7
c. –3, 11
d. none of these

Q5. If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real and less than 3, then :
a. a < 2
b. 2 ≤ a ≤ 3
c. 3 < a ≤ 4
d. a > 4


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jigar_er_civil's picture
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ans

Q2. If one root of the equation ax2 + bx + c = 0 is 3 times other root, then which of the following is true?
a. 3b2 = ac
b. 3b3 = 28ac
c. b2 = 16ac
d. 3b2 = 16ac

if root are x and y

then x+y=(-b/a) and xy=c/a

from data 4x=(-b/a) and 3x^2=c/a

by solving both equation we get 3b^2=16ac

Little Star

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Incognito
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answer

Q1. x2 + ax + b = 0 and x2 + bx + a =0 have a common root, then which of the following is true?
a. a + b =0
b. a + b = 1
c. a + b = -1
d. a + 2b = -3

Let (x-1) is a factor of x2 + ax + b = 0 & x2 + bx + a =0
so 1 will be common root .
den put the value of x in the quation u will get a+b=0
similalr now let Let (x+1) is a factor of x2 + ax + b = 0 & x2 + bx + a =0
so -a+b=-1 & -b+a=-1
by adding these 2 we get 0=-2
which is impossible .

so for all positive roots & negetive roots  a+b will be 0.

try ne damn root .

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