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Quadratic Formula for Finding Roots

If ax2 + bx +...

Question

If $a x^{2} + b x + c = 0$ , then x =

$\frac{b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

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$\frac{- b \pm \sqrt{b^{2} - a c}}{2 a}$

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$\frac{2 c}{- b \pm \sqrt{b^{2} - 4 a c}}$

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None of these

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Solution

The correct option is D
None of these

Try making perfect square the given equation by adding and subtracting $\frac{b^{2}}{4 a^{2}}$
on solving it we'll find
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

Suggest Corrections

Similar questions

If $a x^{2} + b x + c = 0$ , then x =

\int R (x, \sqrt{a x^{2} + b x + c}) d x

I. \sqrt{a x^{2} + b x + c} = t \pm x \sqrt{a}

a > 0;

II. \sqrt{a x^{2} + b x + c} = t x \pm \sqrt{c}

c > 0;

III. \sqrt{a x^{2} + b x + c} = (x - a) t \pm x

a x^{2} + b x + c = a (x - α) (x - β)

α

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

\frac{d x}{x + \sqrt{x^{2} - x + 1}}

t

x ?

\int R (x, \sqrt{a x^{2} + b x + c}) d x

I. \sqrt{a x^{2} + b x + c} = t \pm x \sqrt{a}

a > 0;

II. \sqrt{a x^{2} + b x + c} = t x \pm \sqrt{c}

c > 0;

III. \sqrt{a x^{2} + b x + c} = (x - a) t \pm x

a x^{2} + b x + c = a (x - α) (x - β)

α

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

\int \frac{x d x}{(\sqrt{7 x - 10 - x^{2}})}

x

α, β

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

{lim}_{x \to α} {(1 + a x^{2} + b x + c)}^{\frac{1}{x - α}}

α

β

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

lim x \to α {(1 + a x^{2} + b x + c)}^{\frac{1}{x - α}}

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