The quadratic equation $a x^{2} + b x + c = 0$ will have real and distinct roots if :

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 $b^{2} - 4 a c > 0$
As it's stated from the rule of discriminants. the condition will be
$b^{2} - 4 a c > 0$

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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. STATEMENT -1 : Roots of the quadratic equation

3 x^{2} - 2 \sqrt{6} x + 2 = 0

are same.
STATEMENT -2 : A quadratic equation

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

has two distinct real roots, if

b^{2} - 4 a c > 0

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.

Q. If

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

then the roots of quadratic equation

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

is-

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The quadratic equation ax2+bx+c=0 will have real and distinct roots if :

The correct option is B b2−4ac>0As it's stated from the rule of discriminants. the condition will beb2−4ac>0

The quadratic equation $a x^{2} + b x + c = 0$ will have real and distinct roots if :

The correct option is B $b^{2} - 4 a c > 0$
As it's stated from the rule of discriminants. the condition will be
$b^{2} - 4 a c > 0$