Question

Find the value of k if 3x2-k root 3x+4=0 as real root

Answer 1

Answer:

compare given quadratic equation 3x² - k√3 x + 4 =0

with ax² + bx + c = 0 ,

a = 3 , b = - k√3 , c = 4

according to the problem given ,

roots are equal .

b² = 4ac 

( - k√3 )² = 4 × 3 × 4

k² × 3 = 4 ×3 × 4

k² = 4 × 4

k = √ 4 × 4

k = 4 or k = -4 

~ Abhay

Answer 2

Answer:

The value of k is

$\boxed{\red{\sf\:k\:=\:4}}\:\:\sf\:or\:\:\:\boxed{\red{\sf\:k\:=\:-\:4}}$

Step-by-step-explanation:

The given quadratic equation is

$\sf\:3x^{2}\:-\:k\:\sqrt{3}\:x\:+\:4\:=\:0$

$\therefore\sf\:3x^{2}\:-\:k\:\sqrt{3}\:x\:+\:4\:=\:0\\\\\sf\:Comparing\:with\:ax^{2}\:+\:bx\:+\:c\:=\:0\:,\:we\:get\\\\\sf\:a\:=\:3\\\\\sf\:b\:=\:-\:k\:\sqrt{3}\\\\\sf\:c\:=\:4\\\\\sf\:Now, \\\\\pink{\sf\:b^{2}\:-\:4ac\:=\:0}\sf\:\:\:-\:-\:-\:[\:Real\:\&\:equal\:roots\:]\\\\:\implies\sf\:(\:-\:k\:\cancel{\sqrt{3}}\:)^{\cancel2}\:-\:4\:\times\:3\:\times\:4\:=\:0\\\\:\implies\sf\:3k^{2}\:-\:12\:\times\:4\:=\:0\\\\:\implies\sf\:3k^{2}\:-\:48\:=\:0\\\\:\implies\sf\:3\:(\:k^{2}\:-\:16\:)\:=\:0\\\\:\implies\sf\:k^{2}\:-\:16\:=\:0\\\\:\implies\sf\:k^{2}\:=\:16\\\\:\implies\sf\:k\:=\:\pm\:4\\\\:\implies\boxed{\red{\sf\:k\:=\:4}}\:\:\sf\:or\:\:\:\boxed{\red{\sf\:k\:=\:-\:4}}$

Additional Information:

1. Quadratic Equation :

An equation having a degree '2' is called quadratic equation.

The general form of quadratic equation is

ax² + bx + c = 0

Where, a, b, c are real numbers and a ≠ 0.

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Formula to solve quadratic equation:

$\boxed{\red{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^{2}\:-\:4ac}}{2a}}}$