Question

25xsquare +30x+7, find root by sridharacharya formula​

Answer 1

Zeroes -

$\huge\frac{ - 3 - \sqrt{2} }{5} \& \frac{ - 3 + \sqrt{2} }{5}$

Step-by-step explanation:

25x² + 30x + 7

In the standard form of quadratic equation(ax² + bx + c), here -

• a = 25
• b = 30
• c = 7

So,

Using Sridharacharya formula (commonly known as quadratic formula) -

$\frac{ - b± \sqrt{ {b}^{2} - 4 ac} }{2a} \\ \\ (put \: the \: value \: of \: a.b.c) \\ \\ = > \frac{ - 30± \sqrt{ {30}^{2} - 4(25)(7)} }{2(25)} \\ \\ = > \frac{ - 30± \sqrt{900 - 700}} {50} \\ \\ = > \frac{ - 30± \sqrt{200} }{50} \\ \\ = \frac{ - 30± \sqrt{4 \times 25 \times 2} }{50} \\ \\ = > \frac{ - 30± \sqrt{ {2}^{2} \times {5}^{2} \times 2 } }{50} \\ \\ = > \frac{ - 30±2 \times 5 \sqrt{2} }{50} \\ \\ = > \frac{ - 30±10 \sqrt{2} }{50} \\ \\ = > \frac{ - 3± \sqrt{2} }{5}$

Zero no. 1 -

$\frac{ - 3+ \sqrt{2} }{5}$

zero no. 2 -

$\frac{ - 3- \sqrt{2} }{5}$

hope it helps.

Answer 2

ANSWER:

Given:

• 25x^2 + 30x + 7

To Find:

• Roots of the given polynomial.

Solution:

We are given that,

$\implies 25x^2+30x+7$

We know, using Quadratic Formula,

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

Here, a = 25, b = 30 and c = 7.

So,

$\implies x=\dfrac{-(30)\pm\sqrt{(30)^2-4(25)(7)}}{2(25)}$

$\implies x=\dfrac{-30\pm\sqrt{900-700}}{50}$

So,

$\implies x=\dfrac{-30\pm\sqrt{200}}{50}$

$\implies x=\dfrac{-30\pm\sqrt{2\times10\times10}}{50}$

So,

$\implies x=\dfrac{-30\pm10\sqrt2}{50}$

Taking 10 common,

$\implies x=\dfrac{10\!\!\!/(-3\pm\sqrt2)}{50\!\!\!/}$

So,

$\implies\bf x=\dfrac{-3\pm\sqrt2}{5}$

Therefore,

$\implies\bf x=\dfrac{-3+\sqrt2}{5}\:\:\&\:\:\dfrac{-3-\sqrt2}{5}$