## Complex Number and Quadratic Equations Quiz-24 Assertion - Reasoning Type

Complex numbers and quadratic equations is a segment of maths that deals with crucial theorems and concepts along with various formulae. It comprises of linear and quadratic equations along with roots related to the complex number's set (known as complex roots)..

Q1.  Statement 1: The greatest integral value of λ for which (2λ-1) x2-4x+(2λ-1)=0 has real roots, is 2.
Statement 2: For real roots of ax2+bx+c=0,D≥0.
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Q2. Statement 1: If roots of the equation x2-bx+c=0 are two consecutive integers, then b2-4c=1
Statement 2: If a,b,c are odd integer, then the roots of the equation 4 abc x2+(b2-4ac)x-b=0 are real and distinct
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Q3. Let ax2+bx+c=0,a≠0 (a,b,c∈R) has no real roots and a+b+2c=2
Statement 1: ax2+bx+c>0,∀ x∈R
Statement 2: a+b is positive
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True

Q4. Statement 1: If cos⁡(1-i)=a+ib,where a,b∈R and i=√(-1),then a=1/2 (e+1/e) cos⁡1,b=1/2 (e-1/e)sin⁡1
Statement 2: e=cos⁡θ+isin⁡θ
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Q5. Let fourth roots of unity z1,z2,z3 and z4 respectively
Statement 1: z12+z22+z32+z42=0
Statement 2: z1+z2+z3+z4=0
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Q6. Statement 1: The equation (x-p)(x-r)+λ(x-q)(x-s)=0, where p<q<r<s, has non-real roots
Statement 2: The equation px2+qx+r=0 (p,q,r∈R) has non-real roots if q2-4pr<0
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Q7. Statement 1: If both roots of the equation 2x2-x+a=0(a∈R) lies in (1, 2), then-1<a≤1/8.
Statement 2: If F(x)=2x2-x+a, then D≥0,f(1)>0,f(2)>0 yield-1<a≤1/8.
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Q8. Statement 1: The number of values of a for which (a2-3a+2) x2+(a2-5a+6)x+a2-4=0 is an identity in x is 2
Statement 2: If a=b=c=0, then equation ax2+bx+c=0 is an identity in x
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Q9.  Statement 1: If equations ax2+bx+c=0,(a,b,c∈R) and 2x2+3x+4=0 have a common root, then a∶b∶c=2∶3∶4.
Statement 2: Roots of 2x2+3x+4=0 are imaginary.
•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True
Q10. Statement 1: If z1 and z2 are two complex numbers such that |z1 |=|z2 |+|z1-z2 |, then Im (z1/z2 )=0
Statement 2: arg⁡(z)=0⇒z is purely real

•  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
•  Statement 1 is True, Statement 2 is False
•  Statement 1 is False, Statement 2 is True #### Written by: AUTHORNAME

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