Question

Solve the following Quadratic Equation and express your answer correct to 2 significant figures. 2x² –x – 37= 0​

Answer 1

$\green{\large\underline{\sf{Solution-}}}$

Given quadratic equation is

$\rm :\longmapsto\: {2x}^{2} - x - 37 = 0$

On comparing with ax² + bx + c = 0, we get

$\red{\rm :\longmapsto\:a = 2}$

$\red{\rm :\longmapsto\:b = - 1}$

$\red{\rm :\longmapsto\:c = - 37}$

So, Solution is given by

$\boxed{\tt{ \: \: x \: = \: \frac{ - b \: \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} \: \: }}$

So, on substituting the values, we get

$\rm :\longmapsto\: x \: = \: \dfrac{ - ( - 1) \: \pm \: \sqrt{ {( - 1)}^{2} - 4(2)( - 37)} }{2(2)} \: \:$

$\rm :\longmapsto\: x \: = \: \dfrac{1 \: \pm \: \sqrt{1 + 296} }{4} \: \:$

$\rm :\longmapsto\: x \: = \: \dfrac{1 \: \pm \: \sqrt{297} }{4} \: \:$

$\rm :\longmapsto\: x \: = \: \dfrac{1 \: \pm \: 17.204 }{4} \: \:$

$\rm :\longmapsto\: x \: = \: \dfrac{1 \: + \: 17.204 }{4} \: \: or \: \: \dfrac{1 \: - \: 17.204 }{4}$

$\rm :\longmapsto\: x \: = \: \dfrac{ \: 18.204 }{4} \: \: or \: \: \dfrac{ \: - \: 16.204 }{4}$

$\rm \implies\:x = 4.551 \: \: \: or \: \: \: - 4.051$

Note :-

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:17.204 \:\:}}}\\ {\underline{\sf{17}}}& {\sf{\:\:297.000000 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: 289\:  \: \: \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{342}}}& {\sf{\:\: \: \: \: \: 800 \:  \:  \:  \:   \:  \:  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \:684\:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{34404}}}& {\sf{\:\:160000  \:\:}} \\{\sf{}}& \underline{\sf{\:\:137616\:\:}} \\ {\underline{\sf{}}}& {\sf{\: \:  \:  \:  \:  \:22384 \: \: \: \: \: \: \:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

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Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac

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