Question

find the value of k,if the root of the quadratic equation 3x²–kx+48=0​

Answer 1

Answer:

The value of k is ±24.

Step-by-step explanation:

Given that,

We are given with a quadratic equations, 3x²-kx+48=0, and we need to find out the value of k.

So,

The given equation is 3x² - kx + 48 = 0.

Comparing this equation with ax² + bx +c = 0, we get :

• a = 3
• b = -k
• c = 48.

Now, we know that when the roots of quadratic equation are equal to zero then,

→ b² - 4ac = 0

→ (-k)² - 4 * 3 * 48 = 0

→ k² - 4 * 3 * 48 = 0

→ k² - 12 * 48 = 0

→ k² - 576 = 0

→ k² = 576

→ k = √576

→ k = ±24.

Hence, the value of k is ±24.

Extra information:

Quadratic equation =>

A quadratic equation in the variable x is an equation form ax² - bx + x = 0, where a, b, c are real numbers and a ≠ 0.

Example =>

This is the example of quadratic equation,

9x² + 7x - 2 = 0.

Answer 2

${\pmb{\sf{\underline{Explaination...}}}}$

★ It is given that the root of the quadratic equation is 3x²-kx+48=0 and we have to find out the value of k.

• The value of k is 24

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${\pmb{\sf{\underline{Knowledge...}}}}$

Some knowledge about Quadratic Equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ Discriminant is given by b²-4ac

• Discriminant tell us about there are solution of a quadratic equation as no solution, one solution and two solutions.

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation

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${\pmb{\sf{\underline{Required \; Solution...}}}}$

~ As it's given that the root of the quadratic equation is 3x²-kx+48=0 and we have to find out the value of k. To solve this we have to use the formula of discriminant.

$\begin{gathered}\boxed{\begin{array}{c}\\ \bf \bigstar \: Required \; Solution \\ \\ \star \: \sf{As \: given \: = 3x^2 - kx + 48 = 0} \\ \\ \star\sf \: {Discriminant \: is \: given \: by \: b^2 - 4ac} \\ \\ \star \sf \: {General \: form \: of \: Quadratic \: Equation \: is \: ax^2 + bx + c = 0} \end{array}}\end{gathered}$

Now let's see what to do! Firstly, by using the general form of quadratic equation we get the following,

$\: \: \: \: \: \: \: \: \: \sf Here, \begin{cases} & \sf{b \: is \: \bf{-k}} \\ \\ & \sf{a \: is \: \bf{3}} \\ \\ & \sf{c \: is \: \bf{48}} \end{cases}$

~ Now as it's given that the roots are equal to zero then here we have to use equation of discriminant.

$:\implies \sf b^2 - 4ac = 0 \\ \\ :\implies \sf k^2 - 4(3)(48) = 0 \\ \\ :\implies \sf k^2 - 4(144) = 0 \\ \\ :\implies \sf k^2 - 576 = 0 \\ \\ :\implies \sf k^2 - 576 = 0 \\ \\ :\implies \sf k^2 = 0 + 576 \\ \\ :\implies \sf k^2 = 576 \\ \\ :\implies \sf k = \sqrt{576} \\ \\ :\implies \sf k = 24$

Henceforth, the value of k is 24