## Miscellaneous Problems of quadratice equations - Basic

In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a is not equal to 0. If a = 0, then the equation is linear, not quadratic, as there is no term.

Q1. If x2+2x+2xy+my-3 has two rational factors, then the value of m will be

•   6,2
•  -6,-2
•  6,-2
•   None of these

6,-2

Q2.  If x2-hx-2=0, x2-3hx+35(h>0) has a common root, then the value of h is equal to

•  1
•  2
•  3
•  4

4

Q3.  Minimum value of (a+b+c+d)(1/a + 1/b+ 1/c+ +1/d) is

•   4
•  9
•  16
•   25

16

Q4.  Let f(x) = ax3+5x2-bx+1. If f(x) when divided by 2x+1 leaves 5 as remainder, and f(x) is divisible by 3x-1 then

•  a=24,b=11
•   a=26, b=10
•  a=26,b=12
•  None of these

a=26, b=12

Q5.  The number of solution of the equation |x|=cosx is

•  One
•  Two
•  Three
•  Zero

Two

Q6.  The line y+14=0 cuts the curve whose equation is x(x2+x+1)+y=0 at

•  Three real points
•   One real point
•  At least one real point
•  No real point

One real point

Q7. The number of real roots or x8-x5+x2-x+1=0 is equal to

•   0
•  2
•  4
•  6

0

Q8.  The number of positive real roots of x4-4x-1=0 is

•  3
•   2
•   1
•   0

1

Q9.  The number of negative real roots of x4-4x-1=0 is

•  3
•   2
•   1
•  0

1

Q10.  The number of complex roots of the equation x4-4x-1=0 is

•   3
•   2
•   1
•   0

2

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