If the roots of the quadratic equation $a x^{2} + b x + c = 0$ are all imaginary then which one of the following is true?

b^{2} - 4 a c \geq 0

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b^{2} - 4 a c < 0

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b^{2} - 4 a c = 0

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b^{2} - 4 a c > 0

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Solution

The correct option is B $b^{2} - 4 a c < 0$
Given: The roots of a quadratic equation $a x^{2} + b x + c = 0$ .......(1) are all imaginary.
Then the discriminant of the equation (1) is $< 0$ .
The discriminant of the equation (1) is $b^{2} - 4 a c$ .
Therefore, $b^{2} - 4 a c < 0$ .

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Similar questions

The roots of a quadratic equation $a x^{2} + b x + c = 0$ are given by $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , provided $b^{2} - 4 a c \geq 0$ .

Q. What is the nature of the roots of the quadratic equation

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

if
(a)

b^{2} - 4 a c = 0

(b)

b^{2} - 4 a c < 0

Q. If

b^{2} - 4 a c \geq 0

then the roots of quadratic equation

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

is-

If b² – 4ac = 0 then The roots of the Quadratic equation ax² + bx + c = 0 are given by :

Q. If

b^{2} - 4 a c \geq 0

, then write the nature of roots of a quadratic equation

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

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If the roots of the quadratic equation ax2+bx+c=0 are all imaginary then which one of the following is true?

The correct option is B b2−4ac<0Given: The roots of a quadratic equation ax2+bx+c=0.......(1) are all imaginary.Then the discriminant of the equation (1) is <0.The discriminant of the equation (1) is b2−4ac.Therefore, b2−4ac<0.

If the roots of the quadratic equation $a x^{2} + b x + c = 0$ are all imaginary then which one of the following is true?

The correct option is B $b^{2} - 4 a c < 0$
Given: The roots of a quadratic equation $a x^{2} + b x + c = 0$ .......(1) are all imaginary.
Then the discriminant of the equation (1) is $< 0$ .
The discriminant of the equation (1) is $b^{2} - 4 a c$ .
Therefore, $b^{2} - 4 a c < 0$ .