## Complex Number and Quadratic Equations Quiz-27 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: If z1,z2 are the roots of the quadratic equation az2+bz+c=0 such that Im (z1z2)≠0, then at least one of a,b,c is imaginary
Statement 2: If quadratic equation having real coefficients has complex roots, then roots are always conjugate to each other
•  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 the equation ax2+bx+c=0,0<a<b<c, has non-real complex roots z1 and z2, then |z1|>1,|z2|>1
Statement 2: Complex roots always occur in conjugate pairs
•  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. Statement 1: equation ix2+(i-1)x-(1/2)-i=0 has imaginary roots
Statement 2: If a=i,b=i-1 and c=-(1/2)-i, then b2-4ac<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

Q4. Statement 1: The question –x2+x-1=sin4⁡x has only one solution.
Statement 2: If the curve y=f(x)and y=g(x) cut at one point, the number of solutions is 1.
•  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. Statement 1: If a,b,c,a1,b1,c1 are rational and equations ax2+2bx+c=0 and a1x2+2b1 x+c1=0 have one and only one root in common, then both b2-ac and b12-a1c1 must be perfect squares
Statement 2: If two quadratic equations with rational coefficient have a common irrational root p+√q, then both roots will be common
•  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: If a+b+c=0 and a,b,c are rational, then the roots of the equation (b+c-a) x2+(c+a-b)x+(a+b-c)=0 are rational.
Statement 2: Discriminant of equation (b+c-a) x2+(c+a-b)x+(a+b-c)=0 is a perfect square.
•  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. Let a,b,c,p,q be real numbers. Suppose α,β are the roots of the equation x2+2px+q=0 and α,1/β are the roots of the equation x2+2bx+c=0, where β2∉(-1,0,1)
Statement 1: (p2-q)(b2-ac)≥0
Statement 2: b≠pa or c≠qa
•  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: If (a2-4) x2+(a2-3a+2)x+(a2-7a+10)=0 is an identity, then the value of a is 2
Statement 2: If a-b=0, then ax2+bx+c=0 is an identity
•  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 | z1+z2 |2=|z1 |2+|z2 |2,then z1/z2 is purely imaginary
Statement 2: If z is purely imaginary, then z+z ̅=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
Q10. Let f(x)=-x2+(a+1)x+5
Statement 1: f(x) is positive for some α<x<β and for all a∈R
Statement 2: f(x) is positive for all x∈R and for some real a

•  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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