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

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 \geq 0

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b^{2} - 4 a c < 0

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Solution

The correct option is C $b^{2} - 4 a c \geq 0$
Given, the roots of a quadratic equation $a x^{2} + b x + c = 0$ ........(1) are all real.
Then the discreminant of the equation (1) is $\geq 0$ .
The discreminant of the equation (1) is $b^{2} - 4 a c$ .
So $b^{2} - 4 a c \geq 0$ .

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Similar questions

Q. For the equation

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

which of the following statements is incorrect?
(a) If (b² − 4ac) < 0, the roots are imaginary.
(b) If (b² − 4ac) = 0, the roots are real and equal.
(c) If (b² − 4ac) > 0 and (b² − 4ac) is a perfect square, then the roots are rational and unequal.
(d) (b² − 4ac) < 0, the roots are irrational.

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 :

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

The correct option is C b2−4ac≥0Given, the roots of a quadratic equation ax2+bx+c=0........(1) are all real.Then the discreminant of the equation (1) is ≥0.The discreminant of the equation (1) is b2−4ac.So b2−4ac≥0.

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

The correct option is C $b^{2} - 4 a c \geq 0$
Given, the roots of a quadratic equation $a x^{2} + b x + c = 0$ ........(1) are all real.
Then the discreminant of the equation (1) is $\geq 0$ .
The discreminant of the equation (1) is $b^{2} - 4 a c$ .
So $b^{2} - 4 a c \geq 0$ .