## Nature of 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 is not equal to 0. If a = 0, then the equation is linear, not quadratic, as there is no term.

Q1.  The roots of the quadratic equation 2x2+3x+1=0 , are

•   Irrational
•   Rational
•  Imaginary
•   None of these

Rational

Q2.  Let a, b and c be real numbers such that 4a+2b+c=0 and ab>0 . Then the quadratic equation ax2+bx+c=0 has

•  Real roots
•  Complex roots
•  Purely imaginary roots
•  Only one root

Real roots

Q3.  If a

•   Real and distinct
•  Real and equal
•  Imaginary
•  None of these

Real and distinct

Q4.  The equation (x-a)3+(x-b)3+(x-c)3=0, has

•   All the roots real
•   One real and two imaginary roots
•  Three real roots namely x=a,x=b,x=c
•  None of these

All the roots real

Q5.  If a>0, b>0, c>0 , then both the roots of the equation ax2+bx+c=0

•  Are real and negative
•  Have negative real parts
•  Are rational numbers
•  None of these

Have negative real parts

Q6.  If the roots of the equation x2-15-m(2x-8)=0 are equal then m is equal to

•  -3,5
•   1,4
•  3,5
•  -3,-5

3,5

Q7.  The roots of 4x2+6px+1=0 are equal, then the value of p is

•   1/3
•  3
•  2/3
•  4/3

2/3

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Nature of roots - Basic