For a quadratic equation in the standard form $a x^{2} + b x + c = 0$ , the nature of roots is dependent on the value of ?

b^{2} + 4 a c

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b^{2} \pm 4 a c

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\sqrt{b^{2}} - 4 a c

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b^{2} - 4 a c

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Solution

The correct option is D $b^{2} - 4 a c$
Nature of roots is dependent on the value of determinant and discriminant $= b^{2} - 4 a c$

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Similar questions

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. What are the roots of the quadratic equation

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

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. 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. Find the roots of the quadratic equation

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

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For a quadratic equation in the standard form ax2+bx+c=0, the nature of roots is dependent on the value of ?

The correct option is D b2−4acNature of roots is dependent on the value of determinant and discriminant=b2−4ac

For a quadratic equation in the standard form $a x^{2} + b x + c = 0$ , the nature of roots is dependent on the value of ?

The correct option is D $b^{2} - 4 a c$
Nature of roots is dependent on the value of determinant and discriminant $= b^{2} - 4 a c$