## Complex Number and Quadratic Equations Quiz-26 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 |=1,|z2 |=2,|z3 |=3 and |z1+2z2+3z3 |=6, then the value of |z2z3+8z3 z1+27z1z2 | is 36
Statement 2: | z1+z2+z3 |≤|z1 |+|z2 |+|z3|
•  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 f(x) is a quadratic polynomial satisfying f(2)+f(4)=0. If unity is a root of f(x)=0, then the other root is 3.5
Statement 2: If g(x)=px2+qx+r=0 has roots α,β, then α+β=-q/p and αβ=(r/p)
•  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: If both roots of the equation 4x2-2x+a=0,a∈R lie in the interval (-1,1), then-2<a≤1/4.
Statement 2: If f(x)=4x2-2x+a,then D≥0,f(-1)>0 and f(1)>0⇒-2<a≤1/4.
•  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 a2+b2+c2<0, then if roots of the equation ax2+bx+c=0 are imaginary, then they are not complex conjugates
Statement 2: equation ax2+bx+c=0 has complex conjugate roots when a,b,c are 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
Q5. Statement 1: The equation x2+(2m+1)x+(2n+1)=0, where m and n are integer cannot have any rational roots
Statement 2: The quantity (2m+1)2-4(2n+1), where m,n∈I can never be 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
Q6. Statement 1: If n is an odd integer greater than 3 but not a multiple of 3, then (x+1)n-xn-1 is divisible by x3+x2+x
Statement 2: If n is an odd integer greater than 3 but not a multiple of 3, we have 1+ωn2n=3
•  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 x+(1/x)=1 and p=x4000+(1/x4000) and q be the digit at unit place in the number 2(2n)+1,n∈N and n>1, then the value of p+q=8
Statement 2: If ω,ω2 are the roots of x+1/x=-1, then x2+1/x2=-1,x3+(1/x3)=2
•  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 0<α<(π/4), then the equation (x-sin⁡α )×(x-cos⁡α )-2=0 has both roots in (sin⁡α,cos⁡α)
Statement 2: If f(a) and f(b) possess opposite signs, then there exists at least one solution of the equation f(x)=0 in open interval (a,b)
•  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: Let z1 and z2 are two complex numbers such that |z1-z2 |=|z1+z2 | then the orthocenter of ∆AOB is [(z1+z2)/2] (where O is origin)
Statement 2: In case of right-angled triangle, orthocenter is that point at which the triangle is right angled
•  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 |(zz1-z2)/(zz1+z2 )|=k,(z1,z2≠0), then the locus of z is circle
Statement 2: As |(z-z1)/(z-z2 )|=λ represents a circle, if λ∉{0,1}

•  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 #### Written by: AUTHORNAME

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