Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

The equation x2px+q=0 where p,qR has no real roots if
A.p2>4q
B.p2<4q
C.p2=4q
D.None of these

Answer
VerifiedVerified
500.4k+ views
like imagedislike image
Hint: Given equation x2px+q=0 is of the form ax2+bx+c=0 . This is a quadratic equation. The nature of the roots of a quadratic equation depends on the term b24ac . So let’s check it with the given equation.

Complete step-by-step answer:
Now the given equation is x2px+q=0. Comparing this with the general quadratic equation ax2+bx+c=0 we get a=1, b=-p and c=q. Also it is given that p,qR.
The term that decides the nature of the roots of the equation is,
b24ac(p)24×1×qp24q
Now if p24q<0 then the given equation has no real roots because, roots of the equation is given by,
b±b24ac2a(p)±(p)24×1×q2(p)
p±p24q2p
Now if the term in the square root is negative or less than zero then the roots so obtained are imaginary. Thus the equation has no real roots then.

Note: We will also have a look on other conditions of the nature of the roots .
If b24ac>0The roots are real and unequal.
If b24ac=0The roots are real and equal.


Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for MAHARASHTRABOARD students
PhysicsPhysics
BiologyBiology
ChemistryChemistry
MathsMaths
₹36,600 (9% Off)
₹33,300 per year
Select and buy