Question

Find the roots of the Quadratic Equation 4x^2 = 21x - 5

Answer 1

Here we are given with an equation and we have to find the roots of the Quadratic equation.

• Equation 4x² = 21x - 5

First of all, let's shift all the terms to any one side of the equation,

➝ 4x² - 21x + 5 = 0

Factorising by middle term factorisation,

➝ 4x² - 20x - x + 5 = 0

➝ 4x(x - 5) - 1(x - 5) = 0

Taking (x - 5) common,

➝ (4x - 1)(x - 5) = 0

This means,

• 4x - 1 = 0 or,
• x - 5 = 0

Equating them,

➝ 4x - 1 = 0

➝ 4x = 1

➝ x = 1/4

And,

➝ x - 5 = 0

➝ x = 5

⍒ The roots of the equation is 1/4 and 5 $.$

Tip:

Since the equation can easily be factorsiable by middle term factorisation, I didn't use the quadratic formula with D. This is for avoiding mistakes. If you are not able to factorise, then you can use quadratic formula with D.

Answer 2

Given Equation :-

• $\large\sf{4 {x}^{2} = - 21x - 5}$

To Find :-

• We need to find roots of this equation.

Solution :-

We can write this as,

$\sf{4 {x}^{2} - 21x + 5 = 0}$

We will use Splitting Middle Term Method.

So, Now, Split -21x with -20x - x.

$\implies\sf{4 {x}^{2} - 20x - x + 5}$

$\implies\sf{4x(x - 5) - 1(x - 5)}$

$\implies\sf{(4x - 1)(x - 5)}$

Now, Calculation Of Roots :-

$1) \: \sf{4x - 1 = 0}$

$\implies\sf{4x = 1}$

$\implies\boxed{\bf\red{x = \frac{1}{4} }}$

$\sf{2) \: x - 5 = 0} \\ \\\implies{\boxed{\bf\red {x = 5}}}$

So, Its Roots Are :- 5 and ¼.