Question

find the roots of the equation 4x²-2x+1/4=0 by using the method of quadratic formula​

Answer 1

Answer:

Roots of the quadratic equation are equal and it equals 1/4

Step-by-step explanation:

4x²-2x+1/4=0 (multiply by 4)

16x²-8x+1=0 ; a=16, b=-8 , c=1.

D=$\sqrt{b^{2}-4ac\\ }$

 = $\sqrt{(-8)^{2}-(4)(16)(1) }$

 = $\sqrt{64-64}$

 =0

So the roots are equal.

x= (-b ± D)/2a

x=(8/32)

x=1/4

Answer 2

$\large \maltese \: \: \: \sf \underline{ \underline{Question \: : }}$

• Find the roots of function 4x²-2x+1/4 using quadratic formula or Sridharacharya Formula

${\large{\bull }}\: \: \: \: \mathfrak{ \underline{ \underline{Concepts \: \: about \: \: Sridharacharya \: \: formula} \: \: \: }}_{ \bigstar \star}$

• Usually we use middle term to evaluate the roots of a quadratic equation. But sometimes it gets harder when it comes for a irrational number or any other fractions along with for imaginary numbers. We directly use quadratic equation formula to get the value of roots or zeros, discovered by Indian Mathematician Sridharacharya.
• The Formula is

$\large \longrightarrow \bf \: x = \frac{ - b \pm \sqrt{ {(b)}^{2} - 4ac} }{2a}$

$\bull\: \: \: \: \mathfrak { \underline{ \underline{Let's \: \: solve \: \: this \: \: problem} \: !!}}$

$\large \maltese \: \: \: \sf \underline{ \underline{ Solution\: : }}$

$\longrightarrow\bf \: \: \: \: 4 {x}^{2} - 2x + \frac{1}{4} = 0$

$\longrightarrow \: \: \: \: \sf \: x = \frac{ -(- 2) \pm \sqrt{ {( - 2)}^{2} - 4 \times (4) \times ( \frac{1}{4}) } }{2 \times (4)}$

$\longrightarrow \: \: \: \: \: \sf x = \frac{ 2 \pm \sqrt{4 - 4} }{8}$

$\longrightarrow \: \: \: \: \: \: { \underline{\boxed{ \bf{\:\: \frac{1}{4} \:\:}} \: \: }}_{ \bigstar \star}$