The roots of ax2 - bx - c - 0- a - 0 are real and unequal- if b2- 4ac is -

The correct option is B > 0The roots of the equation ax^2+bx+c=0 are #160; b± #160;√(b^2 4ac)/2a For the equation to have real roots, b^2 4a ...

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Standard X

Mathematics

Nature of Roots

The roots of ...

Question

The roots of $a x^{2} + b x + c = 0, a \neq 0$ are real and unequal, if $b^{2} - 4 a c$ is ___________.

\geq 0

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> 0

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< 0

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None of these

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Solution

The correct option is B > 0
The roots of the equation $a x^{2} + b x + c = 0$ are $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
For the equation to have real roots, $b^{2} - 4 a c \geq 0$
For the equation to have unequal roots, $b^{2} - 4 a c > 0$
$∴$ Option B is correct.

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Similar questions

Q. If the roots of

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

are

α, β

and the roots of

A X^{2} + B x + C = 0

are

(α - k), (β - k)

. Then

(\frac{B^{2} - 4 A C}{b^{2} - 4 a c})

is equal to

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

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

then the roots of quadratic equation

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

is-

Q. If

a, b, c

are real and

b^{2} - 4 a c

is perfect square then the roots of the equation

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

, will be:

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

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The roots of ax2+bx+c=0,a≠0 are real and unequal, if b2−4ac is ___________.

The correct option is B > 0The roots of the equation ax2+bx+c=0 are −b±√b2−4ac2aFor the equation to have real roots,b2−4ac≥0For the equation to have unequal roots,b2−4ac>0∴Option B is correct.

The roots of $a x^{2} + b x + c = 0, a \neq 0$ are real and unequal, if $b^{2} - 4 a c$ is ___________.

The correct option is B > 0
The roots of the equation $a x^{2} + b x + c = 0$ are $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
For the equation to have real roots, $b^{2} - 4 a c \geq 0$
For the equation to have unequal roots, $b^{2} - 4 a c > 0$
$∴$ Option B is correct.