Question

प्रश्न : 3 द्विघात बहुपद x 2 - 53x + 6 का शून्यक क्या होगा?​

Answer 1

Step-by-step explanation:

The given equation

x²-53x+6

where a=1 , b= (-53) and c = 6.

By using the Shridhacharya rule,

$\alpha = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \\ \beta = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a}$

$\alpha = \frac{ - ( - 53) + \sqrt{ {-53}^{2} - 4 \times 1 \times 6} }{2 \times 1}$

$\alpha =\frac{53+\sqrt{2809-24} }{2} \\ \\ \alpha =\frac{53+\sqrt{2785} }{2}\\ \\\alpha =\frac{53+52.77309}{2}\\ \\\alpha =\frac{105.77309}{2}\\ \\\alpha =52.88655$

$\beta =\frac{-(-53)-\sqrt{(-53)^{2}-4*1*6 } }{2*a} \\\\\beta =\frac{53-\sqrt{2809-24} }{2} \\\\\beta =\frac{53-\sqrt{2785} }{2} \\\\\beta =\frac{53-52.77309}{2} \\\\\beta =\frac{0.22691}{2} \\\\\beta =0.11345$

$\alpha =52.88655\\\beta =0.11345$

To check that α and β are correct,

we use the formula (α+β) = -(b/a) and (αβ) = c/a to verify it.

So, ( α+β) = -(b/a)

     (52.88655 + 0.11345)           =              -{(-53)/1}

        53                                      =                 53

And (αβ) = c/a

      (52.88655× 0.11345 )       =             6/1

           5.9999791                   =              6

                  6                            =              6      [ approx same,  ]

Therefore, 52.88655 and 0.11345 is the zero of the given quadratic equation.

THANKS.