## Position of the roots - 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 ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term.

Q1.  If a, b, c are real numbers such that , then the quadratic equation 3ax2+2bx+c has

•   At least one root in [0, 1]
•  At least one root in [1, 2]
•  At least one root in [–1, 0]
•   None of these

At least one root in [0, 1]

Q2. The number of values of k for which the equation x2-3x+k=0 has two real and distinct roots lying in the interval (0, 1), are

•  0
•  2
•  3
•  Infinitely many

0

Q3.  The value of k for which the equation (k-2)x2+8x+k+4=0 has both real, distinct and negative is

•   0
•  2
•  3
•   -4

3

Q4.  If x2-1 is a factor of x4+ax3+3x-b , then

•   a=3,b=-1
•   a=-3, b= 1
•  a=-3,b=-1
•  None of these

a=-3, b= 1

Q5.  If (x-1)3 is factor of x4+ax3+bx2+cx-1 then the other factor is

•  x+2
•  x+1
•  x+3
•  None of these

x+1

Q6.  The complete solution of the inequation x2-4x<12 is

•   x greater than 6 and x less than -2
•   x greater than -6 and x less than 2
•   x greater than 2 and x less than 6
•   x greater than -2 and x less than 6

x greater than -2 and x less than 6

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