Question

please answer this..​

Answer 1

Answer:

the quadratic formula ( SridharAcharya formula)I have attatched here.

in the formula ,

D = b² -4ac..

$.$

Answer 2

★ Concept :-

Here the concept of Quadratic Equation has been used. We see that we are given a quadratic equation and we have to solve it. The best and easiest method to solve this is the method of Quadratic Formula. In this method we shall split the the middle term into two terms which will provide us the common term and thus finally given us the two values of x. These will be the given answer.

Let's do it !!

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★ Formula Used :-

$\;\boxed{\sf{\pink{x\;=\;\bf{\dfrac{(-b)\:\pm\:\sqrt{b^{2}\:-\:4ac}}{2a}}}}}$

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★ Solution :-

Given,

» k² + 5k - 4 = 0

Here the variable term is k. So,

• Here, x = k

• Here, a = 1

• Here, b = 5

• Here, c = -4

We know that,

$\;\sf{\rightarrow\;\;x\;=\;\bf{\dfrac{(-b)\:\pm\:\sqrt{b^{2}\:-\:4ac}}{2a}}}$

By applying values, we get

$\;\sf{\rightarrow\;\;k\;=\;\bf{\dfrac{(-5)\:\pm\:\sqrt{(5)^{2}\:-\:4(1)(-4)}}{2(1)}}}$

$\;\sf{\rightarrow\;\;k\;=\;\bf{\dfrac{(-5)\:\pm\:\sqrt{25\:-\:(-16)}}{2}}}$

$\;\bf{\rightarrow\;\;k\;=\;\bf{\dfrac{(-5)\:\pm\:\sqrt{25\:+\:16}}{2}}}$

$\;\bf{\rightarrow\;\;\red{k\;=\;\bf{\dfrac{(-5)\:\pm\:\sqrt{41}}{2}}}}$

Thus we got two values of k. So,

$\;\bf{\rightarrow\;\;\blue{k\;=\;\bf{\dfrac{(-5)\:+\:\sqrt{41}}{2}\;,\;\dfrac{(-5)\;-\;\sqrt{41}}{2}}}}$

Thus this is the answer.

$\;\underline{\boxed{\tt{Required\;Answer\;=\;\bf{\purple{\dfrac{(-5)\:+\:\sqrt{41}}{2}\;,\;\dfrac{(-5)\;-\;\sqrt{41}}{2}}}}}}$

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★ More to know :-

• Properties of Quadratic Equation ::

• It has two solutions

• The highest degree of the equation is 2

• The graph of the equation intersects x - axis twice.

• Has only one variable to find solution.