Question

Find the root of the following quadratic equation using quadratic formula.
4x²+x-3=0

Answer 1

Answer:

4x^2  + x  - 3 = 0    

a= 4   b =1    c = -3

d= b^2 - 4ac

so

d =  1 - 4(4)(-3)

d= 1+48 = 49

now root d will be 7 so

x = -b + root d/ 2a    and   -b  - root d / 2a

x = -1 + 7/ 8  and      -1 - 7/8

x = 3/4 and -1

Step-by-step explanation:

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

We have 4x² + x - 3 = 0.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The roots and using quadratic formula.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

We know that formula of the quadratic equation :

$\boxed{\bf{x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a} }}}}$

As we know that given quadratic polynomial compared with ax² + bx + c

• a = 4
• b = 1
• c = -3

Now;

$\longrightarrow\tt{x=\dfrac{-1\pm\sqrt{(1)^{2} -4\times 4\times (-3)} }{2\times 4} }\\\\\\\longrightarrow\tt{x=\dfrac{-1\pm\sqrt{1-4\times (-12)} }{8}} \\\\\\\longrightarrow\tt{x=\dfrac{-1\pm\sqrt{1+48} }{8} }\\\\\\\longrightarrow\tt{x=\dfrac{-1\pm\sqrt{49} }{8} }\\\\\\\longrightarrow\tt{x=\dfrac{-1\pm7}{8} }\\\\\\\longrightarrow\tt{x=\dfrac{-1+7}{8} \:\:Or\:\:\dfrac{-1-7}{8} }\\\\\\\longrightarrow\tt{x=\cancel{\dfrac{6}{8} }\:\:Or\:\:\cancel{\dfrac{-8}{8}} }$

$\longrightarrow\tt{\pink{x=\dfrac{3}{4} \:\:Or\:\:x=-1}}$

Thus;

The roots x = 3/4 or x = -1 .