Math, asked by abdlmufi, 8 hours ago

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

Answers

Answered by MrImpeccable
20

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.

Answered by BrainlyArnab
3

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

Step-by-step explanation:

- 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 ( - 4ac),

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

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