Let a- b- c be real numbers with a - 0- Suppose a and 4 a-3 b-2 c have the same sign- Then equation a x2-b x-c-0 cannot have both the roots in the interval-A- 5-6B- 1-2C- 3-4D- 0-1

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

Common Roots

Let a, b, c b...

Question

Let a,b,c be real numbers with a ≠ 0. Suppose a and 4a + 3b + 2c have the same sign. Then
equation ax² + bx + c = 0 cannot have both the roots in the interval.

(1,2)

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

(0,1)

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

(3,4)

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

(5,6)

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

Open in App

Solution

The correct option is A
(1,2)

Note that

If both ∝ and β lie in (1,2), then each of the terms in the right hand side is strictly negative. But this contradicts (1). Hence the given equation cannot have both roots in the interval (1,2).

Suggest Corrections

Similar questions

Let a,b,c be real numbers with a ≠ 0. Suppose a and 4a + 3b + 2c have the same sign. Then
equation ax² + bx + c = 0 cannot have both the roots in the interval.

Q. If

a

and

4 a + 3 b + 2 c

have same sign. Then,

a x^{2} + b x + c = 0, (a \neq 0)

cannot have both roots belonging to

Q. Suppose

a, b, c \in R

a \neq 0

and

4 a - 6 b + 9 c < 0

and

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

does not have real roots, then

Q. Let

a, b,

and

c

be real numbers such that

4 a + 2 b + c = 0

and

a b > 0

. Then the equation

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

has

Q. Assertion :Let

a, b, c

be real such that

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

and

x^{2} + x + 1 = 0

have a common root.

a = b = c

Reason: Two quadratic equations with real coefficients cannot have only one imaginary root common.

Join BYJU'S Learning Program

Let a,b,c be real numbers with a ≠ 0. Suppose a and 4a + 3b + 2c have the same sign. Then equation ax2 + bx + c = 0 cannot have both the roots in the interval.

The correct option is A (1,2)Note that If both ∝ and β lie in (1,2), then each of the terms in the right hand side is strictly negative. But this contradicts (1). Hence the given equation cannot have both roots in the interval (1,2).

Let a,b,c be real numbers with a ≠ 0. Suppose a and 4a + 3b + 2c have the same sign. Then
equation ax² + bx + c = 0 cannot have both the roots in the interval.

The correct option is A
(1,2)

Note that

If both ∝ and β lie in (1,2), then each of the terms in the right hand side is strictly negative. But this contradicts (1). Hence the given equation cannot have both roots in the interval (1,2).