Prove that root of equation ax2-bx-c-0 is -b-b2-4ac2a

Consider #10;the following equation. ax^2+bx+c=0 #10; #10;Divide both #10;side by ,a, we get, #10; #10; #160; x^2+bxa+ca=0 #10; #1 ...

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Standard X

Mathematics

Solving Using Quadratic Formula When D>0

Prove that ro...

Question

Prove that root of equation $a x^{2} + b x + c = 0$ is $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

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Solution

Consider the following equation.
$a x^{2} + b x + c = 0$

Divide both side by ,a, we get,

$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$

${(x + \frac{b}{2 a})}^{2} - \frac{b^{2}}{4 a^{2}} + \frac{c}{a} = 0$

${(x + \frac{b}{2 a})}^{2} = \frac{b^{2} - 4 a c}{4 a^{2}}$

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

Hence, this is the correct answer.

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Similar questions

Q. Prove the root of equation

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

\Rightarrow x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Q. Prove that the roots of

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

are

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

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

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

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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Prove that root of equation ax2+bx+c=0 is−b±√b2−4ac2a

Consider the following equation.ax2+bx+c=0 Divide both side by ,a, we get, x2+bxa+ca=0 (x +b2a)2−b24a2+ca=0 (x +b2a)2=b2−4ac4a2 x=−b±√b2−4ac2a Hence, this is the correct answer.

Prove that root of equation $a x^{2} + b x + c = 0$ is $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$