Math, asked by BrainlyProgrammer, 3 months ago

Solve the following quadratic equation.
7x²+x-3=0​

Answers

Answered by Aryan0123
8

Given Quadratic equation 7x² + x - 3 = 0

For finding the value of x, we apply the quadratic formula.

where:

  • a = 7
  • b = 1
  • c = -3

 \sf{x =  \dfrac{ - b \pm \sqrt{ {b}^{2}  - 4ac} }{2a} } \\  \\

 \implies \sf{x =  \dfrac{ - 1 \pm \sqrt{(1)^{2}  - 4(7)( - 3)} }{2(7)} } \\  \\

 \implies \sf{x =  \dfrac{ - 1  \pm \sqrt{1 - ( - 84)} }{14} } \\  \\

\implies \sf{x =  \dfrac{ - 1 \pm \sqrt{1 + 84} }{14} } \\  \\

 \implies \sf{x =  \dfrac{ - 1 \pm \sqrt{85} }{14} } \\  \\

 \implies \sf{x =  \dfrac{ - 1 \pm \sqrt{25 \times 3} }{14} } \\  \\

 \implies \sf{x =  \dfrac{ - 1 \pm \: 5 \sqrt{3} }{14} } \\  \\

Now there are 2 possible values of x that is:

\boxed{ \bf{x =  \dfrac{5 \sqrt{3}  - 1}{14} \quad  or \quad x =  \dfrac{ - 1 - 5 \sqrt{3} }{14} }}

KNOW MORE:

For solving any given polynomial, there are 3 methods:

  1. Factorising (if possible)
  2. Applying quadratic formula
  3. Completing the square method
Answered by kamalrajatjoshi94
2

Given to Factorise:-

7x²+x-3=0

Formula used:-

 \frac{ - b +  -  \sqrt{ {b}^{2}  - 4ac} }{2a}

Here,

a= 7

b= 1

c= -3

Applying the formula:-

 \frac{ - 1 +  -  \sqrt{ {1}^{2}  - 4(7)( - 3)} }{2(7)}

 \frac{ - 1 +  -  \sqrt{1 +  84} }{14}

  \frac{ - 1 +  -  \sqrt{85} }{14}

 =  \frac{ - 1 +  -9.219}{14}

Hence,

The possible roots are:-

1st root=

  \frac{ - 1  + 9.219}{14}

  = \frac{ 8.219}{14}

 =  \frac{8.22}{14}

=0.587

=0.59

2nd root-

 \frac{ - 1 - 9.219}{14}

 =  \frac{ - 10.219}{14}

 =  \frac{ - 10.22}{14}

= -0.73 (approx)

If we substitute the values of 1st root we get the value 0.0267 which is approximate 0 and if we substitute the 2nd root we get the value 0.0003 which is also approximate equals to 0 hence the given roots are:-

x= 0.59, -0.73

Note:If we don't round off the values we will get the value more close to zero but according to the rule we have to round off so I rounded off it.

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