If the two roots of a quadratic polynomial ax 2- bx - c are negative- which of the following statements holds true-A- a and b are of opposite signs-B- b and c are of opposite signs-C- a- b and c have the same sign-D- a and c are of opposite signs-

The correct option is C a, b and c have the same sign.As the product of the roots ( c/a ) is positive, therefore both a and c are +ve or ve simultaneously As ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Nature of Roots

If the two ro...

Question

If the two roots of a quadratic polynomial $a x^{2} + b x + c$ are negative, which of the following statements holds true?

a and c are of opposite signs.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a, b and c have the same sign.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a and b are of opposite signs.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

b and c are of opposite signs.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B a, b and c have the same sign.
As the product of the roots $(\frac{c}{a})$ is positive, therefore both a and c are +ve or -ve simultaneously
As the sum of roots $(\frac{- b}{a})$ is –ve, if a is +ve, b must be +ve , and if a is -ve , b must be -ve.

Suggest Corrections

Similar questions

Q. Question 9
If the zeroes of the quadratic polynomial

a x 2 + b x + c, w h e r e c \neq 0

are equal then
(A) c and a have opposite signs
(B) c and b have opposite signs
(C) c and a have the same sign
(D) c and b have the same sign

Q. For the quadratic equation

a x^{2} + b x + c = 0

, if

b^{2} - 4 a c > 0

and

a, c

have same sign, then which of the following is true?

(a, b, c \in R, a \neq 0)

Q. For the quadratic equation

a x^{2} + b x + c = 0, a, b, c \in R

and

a c < 0,

then which of the following is true ?

Q. For the quadratic equation

a x^{2} + b x + c = 0; a, b, c \in R,

which of the following is/are true ? (where

Δ = b^{2} - 4 a c

Q. In a quadratic equation

a x^{2} + b x + c = 0

, if

a

and

c

are of opposite sign and

b

is real, then the roots of the equation are

Join BYJU'S Learning Program

If the two roots of a quadratic polynomial ax2+bx+c are negative, which of the following statements holds true?

The correct option is B a, b and c have the same sign.As the product of the roots (ca) is positive, therefore both a and c are +ve or -ve simultaneously As the sum of roots (−ba) is –ve, if a is +ve, b must be +ve , and if a is -ve , b must be -ve.

If the two roots of a quadratic polynomial $a x^{2} + b x + c$ are negative, which of the following statements holds true?

The correct option is B a, b and c have the same sign.
As the product of the roots $(\frac{c}{a})$ is positive, therefore both a and c are +ve or -ve simultaneously
As the sum of roots $(\frac{- b}{a})$ is –ve, if a is +ve, b must be +ve , and if a is -ve , b must be -ve.