Question

x^2-45x+324 solve with quadratic formula​

Answer 1

ANSWER:

To Solve:

• x^2 - 45x + 324

Solution:

We are given that,

$\implies x^2-45x+324$

We know that, by Quadratic Formula,

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

Here, a = 1, b = -45 and c = 324.

So,

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

$\implies x=\dfrac{-(-45)\pm\sqrt{(-45)^2-4(1)(324)}}{2(1)}$

$\implies x=\dfrac{45\pm\sqrt{2025-1296}}{2}$

$\implies x=\dfrac{45\pm\sqrt{729}}{2}$

$\implies x=\dfrac{45\pm\sqrt{27\times27}}{2}$

$\implies x=\dfrac{45\pm\sqrt{27^2}}{2}$

$\implies x=\dfrac{45\pm27}{2}$

So,

$\implies x=\dfrac{45+27}{2}\:\:\&\:\:x=\dfrac{45-27}{2}$

$\implies x=\dfrac{72}{2}\:\:\&\:\:x=\dfrac{18}{2}$

Hence,

$\implies\bf x=36\:\:\&\:\:x=9$

Therefore, value of x is 36 and 9.

Answer 2

$\huge \fcolorbox{red}{maroon}{ \blue{x = 36 \& 9}}$

Step-by-step explanation:

x² - 45x + 324

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

• a = 1
• b = -45
• c = 324

Using the quadratic formula,

$\dfrac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a}$

put the value of a, b & c

$= > \dfrac{ - ( -45) ± \sqrt{ {( - 45)}^{2} - 4(1)(324)} }{2(1)} \\ \\ = > \dfrac{45± \sqrt{2025 - 1296} }{2} \\ \\ = > \dfrac{45± \sqrt{729} }{2} \\ \\ = > \dfrac{45± \sqrt{27 \times 27} }{2} \\ \\ = > \dfrac{45± \sqrt{ {27}^{2} } }{2} \\ \\ = > \dfrac{45 ±27}{2}$

Now,

root(zero) no. 1 -

taking 45+27/2,

$\dfrac{45 + 27}{2} \\ \\ = > \frac{72}{2} = \red{36}$

root no. 2 -

taking 45-27/2,

$\frac{45 - 27}{2} \\ \\ = > \frac{18}{2} = \red{9}$

So the roots for this equation are,

x = 36 & x = 9

.

Note :-

A quadratic equation have only two zeroes.

Sum of zeroes = -b/a

product of zeroes = c/a

To find the roots (zeroes) are real or imaginary -

When discriminant (b² - 4ac),

• b² - 4ac < 0, so roots are imaginary
• b² - 4ac = 0, roots are real and both roots will be equal
• b² - 4ac > 0, roots are real and unequal.

.

Quadratic formula (we used above) is also known as Sridharacharya formula, because he discovered it.

.

hope it helps.