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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Solution

For $a x^{2} + b x + c = 0$ , roots of the equation are represented by,
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

As $b^{2} - 4 a c \geq 0$ , then the roots are real.

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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. If

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

then the roots of quadratic equation

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

is-

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. If

a, b, c

are integers and

b^{2} = 4 (a c + 5 d^{2}), d \in N

, then roots of the quadratic equation

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

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

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If b2−4ac≥0, then write the nature of roots of a quadratic equation ax2+bx+c=0.

For ax2+bx+c=0, roots of the equation are represented by,x=−b±√b2−4ac2aAs b2−4ac≥0, then the roots are real.

If $b^{2} - 4 a c \geq 0$ , then write the nature of roots of a quadratic equation $a x^{2} + b x + c = 0$ .

For $a x^{2} + b x + c = 0$ , roots of the equation are represented by,
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

As $b^{2} - 4 a c \geq 0$ , then the roots are real.